Creation of extremely strong yet ultra-light materials can be achieved by capitalizing on the hishy;eshy;rshy;ashy;shy;rshy;chical design of 3-dimensional nano-architectures. Such structural meta-materials exhibit superior thermoshy;mechanical proshy;shy;shy;pershy;shy;ties at exshy;treshy;meshy;ly low mass densities (lighter than aerogels), making these solid foams ideal for many scientific and techshy;noshy;loshy;gishy;cal applications. The dominant deshy;forshy;mation mechanisms in such “meta-materials”, where individual constituent size (nanometers to microns) is compashy;rable to the characteristic microstructural length scale of the constituent solid, are essentially unshy;known. To harness the lucrative properties of 3-dimensional hierarchical nanostructures, it is critical to assess mechanical properties at each relevant scale while capturing the overshy;all structural complexity.
We present the fabrication of 3-dimensional nano-lattices whose constituents vary in size from several nanometers to tens of microns to millimeters. We discuss the deformation and mechanical properties of a range of nano-sized solids with different microstructures deformed in an in-situ nanomechanical instrument. Attention is focused on the interplay between the internal critical microstructural length scale of materials and their external limitations in revealing the physical mechashy;nisms which govern the mechanical deformation, where competing material- and structure-induced size effects drive overall properties.
We focus on the deformation and failure in metallic, ceramic, and glassy nano structures and discuss size effects in nanomaterials in the framework of mechanics and physics of defects. Specific discussion topics include: fabrication and characterization of hierarchical 3-dimensional architected meta-materials for applications in biomedical devices, ultra lightweight batteries, and damage-tolerant cellular solids, nano-mechanical experiments, flaw sensitivity in fracture of nano structures.

In order for these carbon nanostructures to be used as reinforcing constituents in the advanced composite materials and structures, one needs to assess their structural performance subject to various loading conditions. Such structure performance can be evaluated by mechanical properties such as stiffness, maximum stress and strain to failure, etc. Among numerical analytical work to predict the mechanical properties of the carbon-based molecular architectures, widely and promisingly used are an atomistic modeling, such as molecular dynamic (MD) simulations [1, 2], tight binding MD [3], density functional theory [4], classical continuum mechanics [5] and structural mechanics approach, etc. While many aspects of the carbon nanostructures have been discussed in literature, only a few study has been conducted to predict their mechanical strength subject to various modes of loading such as tension, compression and shear loads, especially for the complicated 3-D carbon nanostructures.
In the current study, we have developed a computational method to predict the mechanical strength of various carbon nanostructures, such as CNTs, graphene sheets, CNT-graphene and CNT-CNT junctioned nanostructures, and have identified their critical failure modes. The prediction method is based on combined molecular mechanics and atomistic molecular dynamics simulations by ensuring a global energy minimum at a given loading level. We have applied the present method to various carbon nanostructures including carbon nanotubes (CNTs), graphene, CNT with defects, CNT-graphene junctioned 3-D nanostructures and pillared graphene nanostructures. We have identified the maximum stress and strain at failure of these carbon nanostructures as well as their critical failure modes. Further, the failures due to defects in mixed chirality carbon nanotubes are also predicted.
1. S. Iijima, C. Brabec, A. Maiti, J. Bernholc "Structural flexibility of carbon nanotubes". J Chem Phys, Vol. 104, No. 5, pp 2089-2092, 1996.
2. B. I. Yakobson, M. P. Campbell, C. J. Brabec, J. Bernholc "High strain rate fracture and C-chain unraveling in carbon nanotubes". Comp Mater Sci, Vol. 8, No. 4, pp 341-348, 1997.
3. E. Hernández, C. Goze, P. Bernier, A. Rubio "Elastic Properties of C and BxCyNz Composite Nanotubes". Phys Rev Lett, Vol. 80, No. 20, pp 4502-4505, 1998.
4. D. Sánchez-Portal, E. Artacho, J. M. Soler, A. Rubio, P. Ordej "Ab initio structural, elastic, and vibrational properties of carbon nanotubes". Phys Rev B, Vol. 59, No. 19, pp 12678-12688, 1999.
5. Y. J. Liu, X. L. Chen "Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element". Mech Mater, Vol. 35, No. 1-2, pp 69-81, 2003

A new ceramic-carbon nanostructured hybrid (86 vol.% ceramics, 14 vol.% carbon) formed from organoclay during pyrolysis is reported. It functions as a reinforcing filler and a binder for carbon/carbon (C/C) composites, which are important as high-temperature lightweight structural materials, as used for reentry vehicles, missiles and aircraft brakes. However, they suffer from high processing cost, which is due to the need to use multiple impregnation-carbonization cycles and methods such as chemical vapor infiltration (CVI) in order to achieve sufficient densification and hence adequate mechanical properties. Alone, the cerami-carbon hybrid can also serve as a high-temperature structural monolith. During pyrolysis, the ordered montmorillonite clay (d₀₀₁ 31.5 Å) is transformed to mullite, cristobalite and disordered clay, and probably amourphous silica as well, allowing the clay part of the organoclay to serve as both binder and reinforcement. The organic part serves as a binder. Although organclay has been investigated extensively for use as a filler in composite materials, particularly polymer-matrix composites, it has not been previously explored for use as both a filler and a binder. The dual functions allow the organoclay to be highly effective for strengthening C/C composites. Thus, a unidirectional C/C composite (50 vol.% fibers, 33 vol.% carbon matrix, 5 vol.% ceramic-carbon hybrid and 12% porosity) exhibiting flexural strength 290 MPa, modulus 55 GPa and toughness 2.9 MPa is obtained by 1000°C 21-MPa hot-press pyrolysis in the presence of mesophase pitch powder, which serves as an additional binder, without densification after the pyrolysis. With the ceramic-carbon hybrid incorporation, the fiber content decreases from 53 to 50 vol.%, but the flexural strength and modulus are increased by 46% and 14% respectively, relative to the composite without the hybrid but with densification. Furthermore, this work has shown that the hot pressing of organoclay in the absence of any other ingredient results in a monolithic material, due to the binding ability of the organoclay. Hot pressing the organoclay alone forms a black monolithic sheet with high thermal stability, electrical resistivity 6 x 10⁶ Omega;.cm, flexural strength 180 MPa, modulus 69 GPa, but low ductility. This work is primarily aimed at (i) investigating the mechanical properties of C/C composites containing organoclay through filler incorporation and elucidating the structure of this multi-scale composite, (ii) investigating the feasibility and effect of conversion of the organic component of organoclay to carbon and the associated feasibility of forming a ceramic-carbon hybrid from organoclay in the absence of any other ingredient, (iii) investigating the feasibility of organoclay serving as both filler and binder, and (iv) investigating the feasibility of using organoclay in the absence of any other ingredient to form a low-cost monolithic high-temperature structural material.

Chemical Vapor Deposition provides a potential for the mass production of graphene. However, the monolayer graphene sheets produced by CVD growth are polycrystalline and the grain boundaries are defects which may change the properties of the material. The elastic properties and breaking strength of free-standing monolayer polycrystalline graphene membranes have been measured by nanoindentation and has shown that the presence of these defects only slightly reduces the breaking strength. Statistical analyses were produced from the experimental fracture load and elastic stiffness. A multiscale model has then been created to reproduce the mechanics of failure of CVD polycrystalline graphene. In this talk, we will focus on the details of the development and results of this multiscale model. It accounts for the natural anisotropy and nonlinearity that is present in graphene. It also accounts for the heterogeneity and fracture mechanisms that are introduced by the presence of the grain boundaries. The fracture mechanisms are characterized by implementing a cohesive zone along the grain boundaries. The parameters that define this cohesive zone have been determined through molecular dynamics based upon typical atomic structures in grain boundaries measured via TEM. Random polycrystalline grain structures have been generated with randomly oriented grains. The nanoindentation experiment mentioned above has been replicated computationally through this model for a large number of these randomly generated membranes. A histogram of distribution of strength at failure is generated and compared with the experimental results. The objective of this model is to provide an understanding of the statistics of failure for CVD grown polycrystalline graphene and compare it to the defect free material.

Graphene and other 2D atomic crystals offer unique new possiblities for creating atomically layered composite materials inspired from biology. Despite the fact that these remarkable properties have been demonstrated at the single molecule level, scaling up from the monolayer properties to large-scale multilayered assemblies has remained elusive due to a lack of understanding of the physical mechanisms that govern the mechanical response of multilayered assemblies at the molecular and mesoscale levels. Coarse-grained molecular dynamics models that permit the study of large-scale systems while preserving molecular level detail hold great promise in this regard. Here we present a mesoscale coarse-grained model of graphene that is able to capture equivalent mechanical features than atomistic force-fields at a fraction of the computational cost, overcoming the length and time scale limitations of atomistic models. The model presented here is parameterized using a strain energy conservation approach. Due to the simplicity of the model&’s force-field, the calibration requires very few of the well-known mechanical properties of graphene, but despite its simplicity, the model is able to quantitatively reproduce graphene&’s mechanical response in the elastic and fracture regimes even outside the calibration range. The hexagonal symmetry of graphene&’s honeycomb lattice is conserved, which we show is crucially important for capturing the anisotropy in the non-linear large deformation regime between the zigzag and armchair directions. The shear rigidity between graphene sheets depends strongly with the rotational angle between the sheets, allowing the model to reproduce the effect known as superlubricity (Ruiz et al., in submission). Finally, we combine our graphene model with our recently developed coarse-graining technique ( Hsu et al. J. Chem. Theory and Comp. 2014) for methacrylate polymers to demonstrate the importance of nanoconfinement effects on the mechanical properties of atomically layered nanocomposites. Our studies pave the way for a theory and simulation informed design methodology for making nanocomposites with intriguing toughening mechanisms.

Material property heterogeneity is present ubiquitously in various natural and man-made materials, such as bones, seashells, rocks, concrete, composites, and functionally graded materials. A fundamental understanding of the structure-property relationships in these material systems is crucial for the development of advanced materials with extreme properties. In this work, a combined experimental and modeling effort is made to examine and control fracture mechanisms in heterogeneous elastic solids. A two-phase laminated composite, which mimics the key microstructural features of many tough biological materials, is selected as a model material. Computationally, finite element analysis with cohesive zone modeling is used to model crack propagation and arrest in the laminated direction. Concurrently, a novel stereolithography-based additive manufacturing system is developed and used for fabricating and testing heterogeneous specimens with well-controlled structural and material properties. The integrative computational and experimental study presented here provides a fundamental mechanistic understanding of the fracture mechanisms in brittle heterogeneous materials and sheds light on the rational design of ultra-tough materials through patterned heterogeneities.

Atomistic simulations are known to be capable in providing molecular-level details of how structural materials respond to applied loading and such approach has been recently extended to the study in construction material, especially concrete. In concrete, it is known that hydrated cement paste is the major constituent dominating the properties of concrete. However, the modeling of hydrated cement paste is a significant challenge because its actual chemical formula has not yet been fully understood. Even though a realistic molecular structure of calcium-silicate-hydrates (C-S-H) has been proposed, such information still cannot be easily applied in practical concrete applications because of the length scale limitations. More importantly, the structure of concrete and even hydrated cement pastes changes at disparate length scales spanning several orders of magnitude. It is well known that the most critical length scale in studying concrete is not at the atomistic scale (several Å). Recent experimental studies on C-S-H gels have indicated that ordered region of C-S-H gel may be present, with a characteristic size of approximately 5 nm. It has been suggested that the results from modeling at molecular scales should be able to be translated into inputs that can predict the mechanical properties of gel at a larger scale. Such inputs can be used to parameterize the interaction potential between groups of atoms, which can be considered as a representative building block of the nanoscale features in cement. In this paper, we are going to demonstrate how the mesoscale modeling of cement matrix can be constructed based on the atomistic modeling of C-S-H, crystalline sand particles, admixtures and additives, with an emphasis on evaluating the interactions between various building blocks identified in nanoscale. It is envisioned that our work forms the basis of the multi-scale methods that can link two scales seamlessly, namely “coarse scale” and “fine scale”, for a more comprehensive understanding of concrete materials.

Nanoporous metals formed via dealloying result in porous materials whose pores and ligaments can be tuned as small as 10 nm. An important structural feature is that dealloying retains the long-range crystalline order of the parent alloy, creating a polycrystalline material in which the individual grains are nanoporous. This structural hierarchy is interesting in the context of mechanics of materials because it can be modeled as a network of micropillars. Micropillars have increased yield stresses over their bulk counterparts, an effect attributed to a decrease in the source length, lambda;, for single arm dislocation sources. The operation stress for these sources is proportional to lambda;^-1, and lambda; is proportional to the pillar diameter. As the pillar diameter decreases its yield strength increases and similar size trends have been seen in nanoporous metals. This strengthening effect is unique because the yield strength is increased without decreasing the ductility of the material. In contrast, material strengthening techniques, such as precipitation hardening or decreasing the grain size, impede dislocation movement and decrease ductility. There is a challenge in testing and studying this effect in nanoporous metals because they are 55-75% void, leading to easy crack propagation and thus appear to be macroscopically brittle. In this work the authors attempt to solve this issue by creating fully dense bicontinuous nanocomposites using a novel dealloying technique, liquid metal dealloying (LMD). LMD is analogous to electrochemical dealloying except that the electrolyte is replaced with a bath of molten metal, and a composite is formed in one step upon cooling. Our work focuses on Cu-X bicontinuous nanocomposites, where X is Ta or W. Parent alloys of Ti-X are immersed in a bath of molten Cu, which has high Ti solubility, but is immiscible with Ta and W. Upon cooling, the resulting nanocomposites are made up of features at several length scales: the ligaments of the refractory form single-crystal micropillar networks with tunable ligament diameter, the copper ligaments are nanocrystalline, and the copper phase also contains CuTi intermetallic precipitates. Mechanical testing of these composites using microtension and compression testing, nanoindentation, and microindentation indicate these materials have very high strengths, correlated to lengthscales within their nanostructure, yet retain significant ductility.

Development of stronger, more conductive, and lighter conductor materials could lower construction costs, reduce energy losses, and increase reliability of HVDC transmission. In this study, an unusually high-strength, high-conductivity, lightweight deformation processed Al/Ca composite conductor was produced by powder metallurgy and severe deformation processing. Additionally, new modeling approaches have been developed to address the microstructure--strength and conductivity relationships in this type of heterogeneous structures. The strength of this composite is much higher than the rule of mixture prediction from conventional composite theory due to the large interface area of fine filaments of sub-micron size. A simple dislocation density based, strain gradient strengthening model was proposed to relate the strain gradient across the interface with the geometrically necessary dislocations emanating from the interface to predict the usually high strength of this type of composite. This strain gradient hardening effect, responsible for the anomalously high strength, is dominant at large deformation true strain because the characteristic microstructure length scale is comparable with the intrinsic material length scale. A simple size dependent conductivity/resistivity model based on the solution of Boltzmann transport equation has been developed for this type of composite considering the scattering effects from interfaces, grain boundaries, impurities and dislocations. The interface and grain boundary scattering effect would be obvious when the microstructure length scale of the phase is comparable with the electron mean free path of the phase. A microstructure “sweet spot” appears to exist if the Ca filaments&’ diameter is below 200 nm but sufficiently larger than 27 nm; Al/Ca composites with such filaments are predicted to deliver very high strength with little degradation of conductivity. The authors appreciate the financial support from ISU Electric Power Research Center, ISU Research Foundation, and Ames Lab Seed Grant through U.S. DOE contract DE-AC02-07CH11358.

Simulations of materials are required for estimating physical or chemical, static or dynamic properties of interest prior to synthesis and experimentation. Polymers are larger in size compared to inorganic materials and therefore, the cost and energy requirement for computation are higher. Therefore, polymers are the class of materials where multi-scaling is necessary for determining their properties on real time and length scales.
Polymers in blends or composites are widely used for packaging food, electronics, pharmaceuticals, etc. In order to design and develop better barrier materials, simulating the diffusion properties of gases such as H₂O and O₂ help understanding and estimating the resultant barrier properties. However, due to the limitation on time scales of ab-initio simulations, it is required to model the system hierarchically and determine the diffusivities comparable to the properties of real systems. Therefore, a blend composite system with two polymers and a nano filler is simulated using molecular dynamics and first principle calculations. The binary interaction energies are determined to estimate interaction parameters between any of the two components. These values are further used to build a system with beads. The unit cell is built with the scaled molecular units known as beads, retaining the ab-initio molecular interactions. The system is subjected to dissipative particle dynamics (DPD) and the diffusion coefficients for H2O and O2 beads are determined through various compositions of the composite systems. Further, the trends from multi-scale simulations are compared to experimental results for validating the simulation approach.

The manipulation and control of phonons is important scientifically in understanding nonlinear propagation, caustic formation and shock interactions, as well as from a technological standpoint, in applications ranging from sound insulation to ultrasonic imaging and shock dissipation. Unique to the challenge in phonon manipulation lies in the material‘s inherently nonlinear response, such as phonon-phonon scattering as well as amplitude dependent shock propagation; this stems from the intriguing structure of the different materials across multiple length scales, from the atomic to the meso-scale, which gives rise to this rich behavior. Phononic metamaterials (PMM) enables one to access certain exotic propagation behavior, such as super-tunneling, negative refraction and super-absorption, by controlling the wave propagation behavior through deliberate structuring at a particular length scale. Furthermore, dynamic behavior in PMM are exploited typically through affine deformation or elastic instabilities, leading to symmetry changes in the structure and hence in the dispersion behavior. However, we propose that, by harnessing the intrinsic nonlinear responses in materials, (occurring at a particular length scale) together with the structural symmetry at targeted length scales, we can arrive at novel methods of controlling wave propagation behavior. One explicit example of this is in spider silk fibers, whihc possess macroscopically uniaxial symmetry. We theoretically and experimentally observed an indirect hypersonic polarization band gap (30%) and importantly, negative index behavior; we further demonstrated that these properties can be dynamically and reversibily tuned with large amplitude strains (up to ±40%). This is attributed to the interactions between the elastic nonlinearity arising between the multi-scale structure (sub 50 nm) of the spider silk constituents and its uniaxial structure at a different length scale(sub 1um). The origin of this band gap is distinct from common mechanism attributed to scattering or hybridization while the negative index behavior arises from the elastic nonlinearity, pointing the way forward to new methods of generating negative index behavior through nonlinearities. This unprecedented result reveals the major role of multilevel structural organization on elastic energy flow and the influence of nonlinearity in the mechanical behavior.
We develop this design principle further and show that by designing the multiple length scales, governing both the intrinsic materials response as well as the wave propagation in various PMMs through symmetry principles, we are able to control the nonlinear wave propagation characteristics ranging from efficient dissipation of shock waves, dynamically reconfigurable phonon polarizers, lens as well as ultracompact sound isolation. This provides an avenue for designing novel systems with tailored and importantly, functionally optimized properties.

Developing materials or systems for low-cost solar cells is critical for clean energy technologies and sustainable energy future. Nonetheless, improving the absorption efficiency of conventional solar cells (which is well below their thermodynamic limit) is a challenging task. One of the candidates that have evolved recently as a promising candidate for solar applications is nanometer sized solid called quantum dot, which has many critical applications in electronics, biomedicine and biotechnology, due their confinement characteristics. The key feature that is used to define their basic behavior is size that restricts the spatial expansion of the electronic wavefunction, thereby producing confinement of electrons and allowing absorption of energy. There are many materials (such as CdSe, PbS, GaAs) that show good confinement characteristics, but they are usually expensive. SiGe quantum dots, which are Si-compatible and thus a cheap alternative to these materials, form dots that are much larger (on the order of 50 nm) in size compared to their single crystalline counterparts (on the order of 5 nm). Consequently, their confinement ability is disregarded. Here, using a multiscale computational framework, we show that heterogeneous distribution of an array of alloy quantum dots, mediated by non-uniform mismatch strain at the interface between the quantum dots and the substrate on which they are grown, leads to substantial confinement of electrons and enhances controllability of the absorption efficiency of QD solar-cells from a mechanics perspective.

Density function theory (DFT) calculations are integrated into a continuum mechanics formulation for simulating macroscale ferroelectric constitutive behavior. Theoretical relations associated with the Hellman-Feynman stress theory are used to guide the energy and electromechanical constitutive relations in the homogenized, continuum approximation of the stored energy function. Challenges associated with addressing uncertainty in length scales between the atomic lattice scale and the continuum mesoscale are treated using stochastic homogenization and Bayesian statistics. This is achieved by quantifying DFT energy, stress, and polarization over a range of constrained lattice dimensions and internal atomic configurations. The DFT energy calculations are fit to a continuum scale stored energy function using Markov chain Monte Carlo algorithms and Bayesian statistics. Probabilities distributions of the material parameters are used to guide the development of stochastic based homogenization of the stored energy. Ferroelectric hysteresis curves are numerically simulated on lead titanate and compared to data in the literature.

The residual stress that develops during thin film growth depends on processes that happen at the triple junction where neighboring grains impinge to form new segments of grain boundary. The resulting stress varies dramatically with the processing parameters and film material. We measure stress development in real time during copper and nickel electrodeposition on uniform as well as lithographically patterned films with varying length scales, deposition rates, and solution concentrations. The results are compared with an analytical model that considers forces and kinetic processes that occur at the triple junction. The model predicts that the steady-state growth stress depends on the combined parameter D/RL, where D is effective atomic diffusivity, R is growth rate, and L is island spacing.

Cephalopods can display dazzling patterns of colors by selectively contracting muscles to reversibly activate chromatophores - pigment-containing cells under their skins. Inspired by this novel coloring strategy found in nature, we design an electro-mechano-chemically responsive (EMCR) elastomer system that can exhibit a wide variety of fluorescent patterns under the control of electric fields. We covalently couple a stretchable elastomer with mechanochromic molecules, which emit strong fluorescent signals if sufficiently deformed. We then use electric fields to induce various patterns of large deformation on the elastomer surface, which displays versatile fluorescent patterns including lines, circles and letters on demand. Theoretical models are further constructed to predict the electrically-induced fluorescent patterns and to guide the design of bioinspired EMCR elastomers. The material and method open promising avenues for creating next-generation flexible displays, optoelectronics, biomedical luminescent devices, and dynamic camouflage skins.

We demonstrate the computational design of solid-state interfaces patterned to achieve templated precipitation of implanted helium (He) by using the intrinsic, internal structure of semicoherent interfaces. Previous modeling has shown that He precipitates at misfit dislocation intersections (MDIs). We develop a set of criteria that MDI distributions must satisfy to promote the precipitation of He into stable linear channels, rather than isolated bubbles, and identify several candidate heterophase interfaces whose MDI distributions satisfy these criteria. Such channels are pathways for the removal of He through outgassing and may be used to mitigate He-induced damage in future structural materials in nuclear energy applications. Our design ensures robustness by providing solution envelopes, rather than discrete optimal solutions, and incorporates synthesis as a constraint.

The ability to control the direction and propagation of heat is of immense use for enhancing the efficiency of energy utilization. Conventional optical lenses, e.g., based on silica glass are prone to low efficiencies at pertinent infra-red (IR)/longer wavelengths, Given the limitations with natural materials, it would be beneficial to engineer composite materials, with augmented attributes for the purpose of heat manipulation. Here, we experimentally show the transient behavior of such thermal metamaterials fabricated through relatively simple multi-layering procedures and how they can be used for thermal energy re-orientation. Multilayered oriented composites constituted from two materials of different thermal conductivities are shown to have the ability to direct conductive heat flux in a given direction Phi; with respect to the applied temperature gradient . The composites behave as an effective media with anisotropic thermal conductivity (κ_ij) due to their sub-structured arrangement of its constituents . We show the development of the thermal flux profiles, recorded at t = 90 s, 150 s, and 210 s, showing the transient bending of the heat flux lines followed by steady state bending of ~ Phi;= 26⁰ and -26⁰ respectively in two such thermal metamaterials. The temperature profiles are captures using thermal infrared camera (FLIR320) . These observations are in excellent accord with previous our theoretical estimates and computational simulations [1,2]. The implications of our study extend nominally to the bending of the heat flux with far reaching implications to the efficient channeling of thermal energy and new varieties of devices, such as thermal concentrators, cloaks, and diffusers.
Reference
[1] Krishna P. Vemuri, P.R.Bandaru, Geometrical considerations in the control and manipulation of conductive heat flux in multilayered thermal metamaterials , Applied Physics letters,103,13311.
[2] Krishna P. Vemuri, P.R.Bandaru, Anomolous negative refarction in thermal metamaterials, Applied Physics letters,104,083901.

Indentation contact at scales in the micron and submicron range, as is commonly encountered in nanoindentation testing, often involves unusual deformation phenomena. One of these is indentation pop-in, in which contact deformation transitions from purely elastic to elastic-plastic with a large burst of dislocation activity. In this presentation, a simple stochastic description for nanoindentation pop-in is developed based on how close the contact is to a pre-existing dislocation, a behavior that becomes increasingly important as the size of the contact approaches the average dislocation spacing. If there are no dislocations near the contact, plasticity commences only when a dislocation is homogeneously nucleated at the theoretical strength of the material. When pre-existing dislocations are close to the contact, pop-in occurs by activation of the dislocation, with the load needed to so depending on the distance from the contact to the dislocation. A simple stochastic model based on a random distribution and orientation of dislocations is developed to describe these phenomena. The model is tested by comparing its predictions to the dependence of nanoindentation pop-in loads on indenter radius for highly annealed single crystals of molybdenum. The model predicts not only the observed size dependence of the strength, but the size dependence of the scatter as well.

The rapid development of synthesis and characterization of materials with feature sizes at nanoscale as well as unprecedented computational power have brought forth a new era of materials research in which experiments, modeling and simulations are performed side by side to probe the unique mechanical properties of nanostructured materials. Here we report on our recent studies on deformation and fracture in nanotwinned materials, including the maximal strength of nanotwinned metals with equiaxed grains, crack bridging nanotwinned thin films, twin-spacing-induced ductile-brittle transition in nanotwinned nanopillars, fully reversible plastic deformation in penta-twinned nanowires, plastic anisotropy in columnar-grained nanotwinned metals, hierarchical gradient nanotwinned steel and nanotwinned aragonite lamellae in conch shell. In each study, there has been a strong synergy between theory and experiment, with new experimental findings driving advances in modeling and simulations, and new theoretical insights suggesting new experimental studies. The discussions will be organized around the current understandings based on existing experimental and theoretical efforts, as well as the outstanding questions that require further studies in the future.

Nanotwins readily form in numerous fcc metals with low stacking fault energy (SFE). However, growth twins rarely form in Al due to its high SFE. Here, by using thin inter- or buffer layers of a low SFE fcc metal (Ag), we overcome the SFE barrier and successfully grow high-density coherent and incoherent twin boundaries into Al [D. Bufford et al, Materials Research Letters, 1 (2013) 51-60; http://dx.doi.org/10.1080/21663831.2012.761654.]. We identify three mechanisms that enable growth twin formation in Al, and demonstrate enhanced mechanical strength in twinned Al. Furthermore we will show that epitaxial Ag/Al multilayer films have high hardness (up to 5.5 GPa) in comparison to monolithic Ag and Al films (2 and 1 GPa). High-density nanotwins and stacking faults appear in both Ag and Al layers, and stacking fault density in Al increases sharply with decreasing individual layer thickness, h. Hardness increases monotonically with decreasing h, and no softening occurs. In comparison, epitaxial Cu/Ni multilayers reach similar peak hardness when h asymp; 5 nm, but soften at smaller h. High strength in Ag/Al films is primarily a result of layer interfaces, nanotwins, and stacking faults, which are strong barriers to transmission of dislocations. This research is funded by DOE-Office of Basic Energy Sciences.

Strengthening by introducing nanoscale twins has recently received much attention. In particular, nanoscale twins produced by severe plastic deformation processing in austenitic stainless steels enhance the strength and ductility simultaneously. However, the role of mechanically introduced twins in the plastic deformation process has yet to be clarified. Coupled tensile testing using the micrometer-sized specimens with EBSD examinations enable one to elucidate the interaction of mobile dislocations with preexisting twins in the plastic deformation process of the stable austenitic steel. In the present study, the plastic deformation behavior was mesoscopically examined in uniaxial tension testing using micrometer-sized specimens to clarify the impact of the presence of mechanical twins on the strength and plasticity of the austenitic stainless steel. The material used in this study was a single crystalline Fe#8210;18Cr#8210;16Ni (mass%) austenitic steel. Discs with a diameter of 9.5 mm and a thickness of 0.85 mm were processed by high-pressure torsion (HPT). Mechanical twins were introduced by the HPT processing under an applied pressure of 6 GPa for 0.5 turns at room temperature. Specimens for micro-tension testing with a gauge section size of 20 × 20 × 50 mu;m³ were fabricated by focused ion beam (FIB) machining. Three specimens having mechanical twins (tw1, tw2, and tw3) and a single crystalline (sc) specimen were prepared. The directions perpendicular to the twin planes were arranged at an angle of approximately 75° with respect to the loading directions. The microtension test with a micro-gluing grip was conducted at a crosshead speed of 0.1 mu;m s^-1 at room temperature in laboratory air. After failure, a longitudinal cross section was fabricated by FIB machining and was examined by EBSD analysis. The yield stresses in the tw specimens were determined to be 560#8210;770 MPa, which is more than twice higher than 250 MPa of the sc specimen, whereas the elongation-to-failure in the former was 20%#8210;40%. In the tw1 specimen, which exhibited the highest strength, it was observed that the operative slips were impeded by the preexisting twins. On the other hand, the stress#8210;strain behavior in the tw2 specimen indicated some stress drops. These corresponded to the extension of the twin regions. In the tw3 specimen, slips transferred across the twin boundaries. The EBSD analysis showed that the slip systems with the highest Schmid&’s factors in the matrix and twin were operative in the same direction on the twin plane. Therefore, the strength and plasticity of the stable austenitic stainless steel was strongly dependent on the interaction between the mobile dislocations and the twins.

Organic thin-film polymers have the potential for photovoltaic and flexible electronic applications. However, charge transport is highly sensitive to the mechanical behavior of semi-crystalline semiconducting conjugated polymers, such as blend films of poly(3-hexylthiophene) (P3HT) and a fullerene, phenyl-C₆₁-butyric acid methylester (PCBM). An integrated computational and experimental approach is used to identify the dominant microstructural characateristics at different physical scales that would affect both the mechanical behavior and strength and electrical properties of P3HT/PCBM thin films. The computational finite-element approach is based on a recently developed microstructural approach that represents the polymer microstructure as a four-phase model that is physically representative of crystalline domains, an amorphous interphase, tie-chain bridging regions, and PCBM particles. The crystalline phase is modeled with dislocation-density based crystalline plasticity, the amorphous interphase is modeled as a viscoplastic region, the inter-aggregate tie chains are modeled with finite elasticity, and the fullerene are modeled with a finite-elasticity approach that accounts for the high strength carbon (C-C) bonds. The experimental approach combines polymer thin film mechanics and optoelectronic device measurements along with detailed morphological characterization of how cracks can form in the thin films. Based on this approach, the fundamental effects of intralamella crystalline disorders, amorphous chain entanglements, and P3HT edge-on and face-on interfacial orientations can be used to provide new insights between mechanical and electrical behavior.

Material properties for composite structures, such as biological materials and advanced polymers, can be found using multiple techniques and at different length scales. Due to the need to reconcile measurements at multiple scales, various techniques for multiscale modeling are presented. One imaging technique, magnetic resonance elastography, is a non-invasive imaging method to determine tissue properties in vivo. The process of elastography involves the inversion of a nonlinear problem, which necessitates assumptions about the underlying material. In order to improve the fidelity of the elastographic techniques, a finite element model describing the micromechanics of the microstructure of the brain is presented. To demonstrate our approach, a two-dimensional representation of a periodic array of myelinated axons embedded in homogeneous glial matrix is modeled. Confirmation of the numerical codes and a homogenization scheme is carried out via simple test cases. Due to architectural similarities between axonal white matter in the brain and fiber composite materials, the same technique is implemented for modeling of a Kevlar polymer fiber. For the fiber, a representative nanoscale cell for Kevlar fibers is developed that captures the fibril and microfibril structures. In this regard, a finite element model that describes the nanoscale structure of Kevlar fibers was devised to predict their macroscale response. As with the biological materials, it is important to characterize the effects of changes to the microscale behavior and geometry on the macroscale response. To this end, sensitivity analyses are performed to inform areas of future experimental design, research, and development. By using multiscale techniques in combination with relatively simple microscale models, it is possible to perform many calculations in a short amount of computational time, lowering both the cost and time investment for complex models. In addition, by implementing similar techniques and geometry for differing materials, it is relatively straightforward to develop multiuse, high fidelity models.

The ongoing goal of tissue engineering is to produce tissues that biologically and mechanically duplicate the native tissues they are to replace. An important step is creating elastomeric scaffolds that mimic the anisotropic, non-linear, large deformation mechanical behavior of the native tissues. The purpose of this study is to use computational models to explore the range of macroscopic material behaviors that are achievable from the domain of producible microstructural geometries and elastomeric fiber properties. This is an essential first step in developing the ability to design engineered tissues that mimic native tissue behavior.
Many engineered tissue scaffolds consist of layers of dense, long-fiber networks. Experiments have shown that it is possible to create scaffolds that behave similarly to native tissues, and simulations have shown that this behavior is strongly influenced by the evolution of the complex microstructural geometry of the underlying fibrous network. Unfortunately, although manufacturing process parameters can be adjusted to produce a wide variety of network geometries, and thus material behaviors, there is still no known procedure for selecting parameters that produce scaffolds with desired material behaviors. For a given fiber material, this procedure requires three steps: (1) Characterize the complex network geometry; (2) Find the scaffold geometry that results in the desired behavior; (3) Find the parameters that produce the needed geometry and thus the desired macro-level response. We present a complete framework for this approach.
We characterize the geometry as the first critical step in linking process variables to material behavior. We show that two easily measured geometric quantities provide a mechanically meaningful description of the complex network geometry. We also generate simulated geometries possessing specified values of these key quantities using a random walk procedure that mimics the manufacturing process. This representation is an improvement over currently-used straight fiber representations, since fiber contacts and curvature are accurately represented, and the resulting finite element mesh has a similar appearance to real scaffolds. We show the results of non-linear, large-deformation, micromechanical simulations performed on a wide range of geometries. These simulations capture important effects, such as fiber straightening and rotation, and the formation of long-range structures extending into the mesoscale. We demonstrate that a wide variety of behaviors are achievable, from very soft to very stiff, isotropic to highly anisotropic, and linear to strongly non-linear, all solely from alterations in fiber geometry with no change in intrinsic fiber behavior. We hope that insights gained from our simulations will be used to guide the design of scaffolds and selection of process variables so that the resulting engineered tissues mimic the non-linear mechanical behavior of the native tissues.

Aramid fibers owe their high tensile strength and stiffness to their hierarchical fibrillar structure. The synergistic effect of individual fibrils comprising an aramid fiber and the interfibrillar interactions determine the strength of an individual fiber. In order to determine the existence and role of statistical defects in failure initiation of aramid fibers, quasi-static tensile tests were performed with individual fibers of different molecular compositions and gauge lengths in the range of 100 µm - 10 mm. The experimental results pointed out to a relative insensitivity of the tensile strength to the fiber gauge length. Gauge length insensitivity combined with observations through scanning electron and atomic force microscopes in addition to X-ray diffraction studies suggested that failure initiation is governed by processes and/or flaws active at length scales well below the micron scale. Therefore, differences in tensile strength between different types of aramid fibers studied in this work are attributed to interfibrillar interactions. The magnitude of the latter was assessed by longitudinal crack growth experiments with individual fibers, as interfibrillar interactions are expected to be similar to the van der Waals interactions between the hydrogen bonded macromolecular sheets comprising the aramid fibers. Initial fracture experiments have shown stable crack propagation under relatively constant force taking place for very large lengths of individual fibers. Cohesive energy measurements obtained thereby will be presented for two types of aramid fibers designed to provide high tensile strength.

Hydrogels have applications as diverse as scaffolds for tissue engineering, vehicles for drug delivery, actuators for optics and fluidics, and model extracellular matrices for biological studies. The scope of hydrogel&’s applications, however, is often severely limited by their mechanical behavior. For example, injury and disease of load-bearing tissues such as articular cartilages and spine disks have huge impacts on both millions of peoples&’ wellbeing and a multi-billion-dollar biomaterial industry, posing critical healthcare challenge to our aging society. However, since most synthetic hydrogels are mechanically weak and brittle, current replacements for injured or diseased load-bearing tissues have to rely on metals and rigid plastics, sacrificing hydrogels&’ bioactivity and flexibility for mechanical robustness.
Inspired by the mechanics and structures of tough biological tissues, we propose that a general principle for the design of tough hydrogels is to implement two mechanisms for dissipating mechanical energy and maintaining high elasticity in hydrogels [1-4]. A particularly promising strategy for the design is to integrate multiple pairs of mechanisms across multiple length scales ranging from nanometers to millimeters into a hydrogel [2,4]. Guided by our theoretical model and design principle, we develop a new hydrogel system with extremely high toughness as well as capability of stem-cell encapsulation. Applications of the tough and bioactive hydrogels will be further discussed, for example, by 3D printing them into various prototypes for tissue regeneration [4].
Reference
[1]. J. Sun et al, Nature, 489, 133 (2012)
[2]. X. Zhao, Soft Matter, 10, 672 (2014)
[3]. I. Liao et al, Advanced Functional Materials, 47, 5833 (2013)
[4]. S. Lin et al, Soft Matter, In press (2014)

The tongue of the C. Stelleri is provided with numerous rows of highly mineralized teeth composed of a soft organic chitin matrix and hard magnetite rods. The shell of the tooth is characterized with the highest modulus and hardness of any known bio-mineral. Similar to other biological materials (i.e. nacre and conch), the tooth is provided with mineral bridges, nano-scale asperities and roughness, and a microstructure composed of stiff piled rods wrapped in a matrix of soft organic material. Despite the advanced microscopic techniques used today, not much has been said about the influence of the geometrical aspects in the complex microstructure. To test the effect of the geometrical parameters in the mechanical properties measured by indentation test (E_r, H), a set of biomimetic designs composed of stiff rods surrounded by weak interfaces have been manufactured. Post-indented samples show that it is possible to replicate the localized damage and crack tolerance observed in the tooth with rapid prototypes. Results indicate that a variation in the aspect ratio of the rods can lead to a 50% increase in the stiffness and a 30% increase in the hardness measured. It is also observed that the rod like microstructure can mitigate catastrophic failure with interface cracking, rod failure and material debonding. Computational models suggest that inelastic deformation of the rods at early stages of indentation can vary the resistance to penetration, in which the mechanical behavior of the system is influenced by interfacial shear strain and high plastic stresses in the rods. It is also shown that the design of the rod-like microstructure can be tailored to abrasion resistant or fracture tolerant materials. In this study, it is demonstrated that additive manufacturing is a useful technology that can be used to unveil the mechanical behavior of intrincated microstructures.

Cellulose nanocrystals (CNCs) are ubiquitous in some of nature&’s toughest biological nanocomposites such as wood and bacterial cell walls [1] and exhibit outstanding mechanical properties rivaling those of synthetic materials such as Kevlar [2]. Whereas the impressive elastic properties of CNCs have been well characterized at the macroscale, a molecular level understanding of how cellulose-based materials achieve high fracture toughness with relatively weak secondary interactions remains to be explained. Here we summarize our work focused on understanding the molecular interactions within individual CNCs, revealing key information on the types of molecular mechanisms at work in these systems, as well as size effects that govern the optimal size of CNCs from a fracture perspective [3]. In addition, we present new analyses based on atomistic steered molecular dynamics (SMD) simulations and theoretical considerations to calculate the fracture energy of interfaces between CNCs. In this work, CNCs of “elementary size” (36 individual cellulose chains arranged hexagonally [4]) are studied as commonly found in wood and other biological structural materials. We investigate the mechanics of (200)-(200) and (110)-(110) interfaces in both perpendicular (i.e. pulling apart) and parallel (i.e. shearing) loading. Pull-apart simulations show that the (110)-(110) interface has a higher fracture energy than the (200)-(200) interface, which is attributed to strong hydrogen bonding for (110)-(110) compared to van der Waals interactions for (200)-(200). Shearing simulations show a common mechanism and common shape of the shear energy landscape for both the (110)-(110) and (200)-(200) interfaces. During shearing, fibrils move between local energy minima along the interface while also exhibiting an underlying increase in energy. The distance between these energy minimums is observed to be a function of the surface geometry, while the magnitude of the energy barrier that must be overcome to reach the next minimum is a function of the dominant molecular interaction mechanism and disparate cooperative length scales that arise from the nature of chemical interactions. Our simulations inform analytical mesoscale traction - separation models that accurately capture the complex energy landscape of the mechanical behavior of CNC elementary fibril interfaces. Additionally, our studies indicate new opportunities for creating tough materials by utilizing the size and geometry dependent interfacial properties nature's most common building block in heterogeneous structural materials.
References:
1] Fratzl, P.; Weinkamer, R. Prog. Mater. Sci. 2007, 52 (8), 1263minus; 1334.
[2] Moon, R. J.; Martini, A.; Nairn, J.; Simonsen, J.; Youngblood, J. Chem. Soc. Rev. 2011, 40 (7), 3941minus;3994.
[3] Sinko, R.; Mishra, S.; Ruiz, L.; Brandis, N.; Keten, S. ACS Macro Letters 2014, 3, (1), 64-69.
[4] Habibi, Y.; Lucia, L. A.; Rojas, O. J. Chem. Rev. 2010, 110 (6), 3479minus;3500

Many natural and biomimetic platelet-matrix composites - such as nacre, silk and clay-polymer - exhibit a remarkable balance of strength, toughness, and/or stiffness, which call for a universal measure to quantify this outstanding feature given the structure and material characteristics of the constituents. Analogously, there is an urgent need to quantify the mechanics of emerging electronic and photonic systems such as stacked heterostructures, which are composed of strong in-plane bonding networks but weak interplanar bonding matrices. Herein, we present the development of a unified framework to construct a universal structure-material-property diagram that decodes the interplay between various geometries and inherent material features in both platelet-matrix composites and stacked heterostructures. Validated by several 3D-printed specimens and a wide range of natural and synthetic materials across scales, this universally valid diagram has important implications for science-based engineering of numerous platelet-matrix microstructures and stacked heterostructures while significantly broadening the spectrum of strategies for fabricating new composites through incorporating contrasting platelets. Given the symposium theme of “hellip;structure-property relationships”, this work opens up several new opportunities to further extend the proposed diagram to include locking mechanisms, stacked multi-heterostructures, extrinsic hierarchical toughening processes, etc. to identify and delineate new boundaries and overlaps in mechanistic processes of platelet-matrix microstructures with the goal of unveiling other mysteries in multi-phase multi-functional materials

Scale like structures often found on fish, amphibians and reptiles have evolved to give protection to the organism from external mechanical threats while maintaining light weight and other biological functions. This evolutionary solution for protection is markedly different from the traditional armor designs which often rely on monolithic, composite, layered or reinforced construction. In this work, we investigate the distinct mechanical advantage that originates from these scales which arise in addition to their own material non-linearity especially during bending response due to self-contact - a relatively novel meso-structural level mechanism. We find that these scales completely change the otherwise linear response of an elastic substrate into a highly complex behavior exhibiting stiffening and complete rigid locking during bending loads as the deformation proceeds. Interestingly, these effects were perceptible even in the small strain regime where traditional material nonlinearities are negligible. In this work we unify these effects using a kinematic phase map and provide analytical and finite element based numerical models as well as qualitative experiments. We identify the geometrical parameters which are especially responsible for controlling the extent of nonlinearity. In addition, we also identify the role of inter-scale friction in altering the effect of the bending response. Next, in addition to bending we also carry out indentation experiments and discover an induced anisotropy of the indented region in addition to an expected increase in contact stiffness due to the presence of scales. This anisotropy is at a structural and not the lower material level of the scale which are known to exhibit naturally highly anisotropic behavior during penetration tests. Thus in this study, we show that meso level scale structures are sufficient to endow complex nonlinear mechanical behavior to an otherwise linear elastic substrate. We also establish scaling relations with respect to scale geometry, scale inclination and skin elasticity which can aid in engineering a real armor system against specific environmental or agent based threats.

Through the process of biomineralization, nature has combined organic and inorganic constituents to create sophisticated functional heterogeneous materials. These structures are often hierarchical in nature and exhibit precise organization of individual components from the macro- down to the nano-scale. Nature&’s ability to control this assembly has resulted in a variety of unique materials that exhibit a wide range of mechanical properties. One example of this is the stomatopod dactyl club, a multiphase bio-composite material that exhibits exceptional damage tolerance from high energy loading events. Here, we investigate the ultrastructural and mechanical features of the dactyl club exocuticle. We identify domains consisting of an oriented crystalline hydroxyapatite mineral phase, which exhibits rod-like and particle morphology. Additionally, this mineral phase is templated by an underlying organic scaffold composed of a unique arrangement of chitin fibers. This ultrastructure results in a stiff and hard outer layer for delivering damaging blows and protecting the club&’s soft interior. These findings as well as further investigation of the growth mechanisms of the dactyl club will provide insights into the formation of composite materials that exhibit well-defined morphology and exceptional impact resistance.

Experimental studies on polycrystalline materials have demonstrated remarkable improvements in materials properties through the control of grain boundary network structure. These three-dimensional networks of quasi-two-dimensional interfaces strongly influence a host of materials properties including mechanical, mass transport, and electronic properties. Variations in the structure of individual grain boundaries can lead to differences in materials properties that span orders of magnitude. This broad spectrum of grain boundary properties makes grain boundary networks strongly heterogeneous and presents a vast and largely unexplored design space that is ripe for materials discovery. Using spectral methods in the context of a statistical description of grain boundary network structure, we present mathematical tools that facilitate design and optimization of grain boundary networks for specific applications. These tools incorporate structure-property relationships that obtain at the local grain/grain boundary level with scale-bridging homogenization relations that permit the prediction of macroscopic effective properties. These methods are applicable to arbitrary materials and allow for rigorous optimization of multiple materials properties simultaneously. As an example, we present a case study in which mechanical and transport properties compete and find an optimal microstructure under certain assumptions.

Heterogeneity is prevalent in almost all solids at some length scales, but it is a challenging task to determine its macroscopic implications, particularly in the context of fracture. Consequently, the understanding of the relation between macroscopic toughness and the microstructural details of a solid remains elusive, which severely limits our ability to design tougher materials for use in practical applications. This talk will discuss the development of a notion of effective toughness in heterogeneous media using a novel boundary condition, named surfing boundary condition. It is found that macroscopic toughness is very different from the weighted surface area of the crack set. Results also indicate that elastic heterogeneity alone can have a profound influence on toughening, and it can induce toughening asymmetry depending on the direction and sense of crack propagation. The findings provide critical insights for designing materials with improved mechanical properties.

Recent advances in manufacturing allow fabrication of multi-phase cellular materials with unprecedented topological complexity. The powerful and rigorous technique of topology optimization provides the perfect tool to optimally arrange the layout of a number of phases in a hierarchical design to achieve unprecedented combination of properties. Although stiffness optimization of lightweight cellular materials and structures made of a single constituent phase has been extensively investigated, the application of topology optimization to more complex objective functions and multi-phase cellular material systems is still in its infancy. In this presentation, we will discuss the optimal design of metal/elastomer periodic cellular materials for maximum vibration damping, where ideal combinations of high stiffness, low density, and high loss coefficient are sought. Two design variables are used to define the three-phase microstructure (metal, elastomer and void), and existing penalization approaches are extended to this three-phase system to achieve complete phase separation. The effective stiffness of the unit cell is easily calculated with homogenization theory. The Bloch-Floquet approach is utilized to analyze the dispersion characteristics of the multi-phase cellular medium under wave propagation and subsequently estimate the damping capacity of the periodic architecture. The effect of wave propagation direction and frequency on the optimal design is discussed

Challenges in addressing length and time scale transitions in models for inelastic behavior of metals with hierarchical heterogeneous structure will be identified and discussed in the context of (i) scale bridging in terms of hierarchical and concurrent multiscale modeling and (ii) scale-specific modeling with bridging via informatics and decision-based design. The former supports modeling of material response at various length and time scales and the latter supports multilevel design of materials. This talk will focus on several key challenges that hinder multiscale models for metallic polycrystals, including the role of grain/phase boundaries in nucleation and slip transfer for grain sizes from the nanoscale to the micron scale, development of dislocation substructure under non-equilibrium conditions, dislocation density based constitutive relations for higher order continua in the submicron length scale regime, and the reduction of model degrees of freedom under coarse-graining. The relation between multiscale modeling and multilevel materials design is discussed, with the former providing two-scale transitions that minimize uncertainty in providing decision support for materials design.

Ductile fracture in metallic alloys often follows a multi-step failure process involving void nucleation, growth and coalescence. Voids nucleate from inclusions and second phase particles due to decohesion or fracture of these particles, grow due to increased deformation, and coalesce to form microscopic cracks and to propagate the main crack. Based on the fracture mechanism, a straight-forward approach to simulate ductile failure process is to model individual voids explicitly using refined finite elements. However, due to sizeable difference between the characteristic length scales involved in the material failure process and the dimensions of the actual structural component, it is impractical to model every void in detail in structure failure analysis, especially for situations involving extensive crack propagation. For this reason, various forms of porous material models have been developed to describe void growth and the associated macroscopic softening during the fracture process. One of the major drawbacks of the Gurson-type porous plasticity models is the inability of these models to predict material failure under low stress triaxiality, shear dominated conditions. This talk summarizes our recent efforts to address this issue by combining the damage mechanics concept of Lemaitre with the Gurson-type porous plasticity model. In particular, the widely adopted Gurson-Tverggard-Needleman (GTN) model is extended by coupling two damage parameters, representing the volumetric damage (void volume fraction) and the shear damage, respectively, into the yield function and flow potential. The effectiveness of the new model is illustrated through a series of numerical tests comparing its performance with existing models. The current model not only is capable of predicting damage and fracture under low (even negative) triaxiality conditions but also suppresses spurious damage that has been shown to develop in earlier modifications of the GTN model for moderate to high triaxiality regimes. Finally the modified GTN model is applied to predict the ductile fracture behavior of a beta-treated Zircaloy-4 that shows tension-compression asymmetry by coupling the proposed damage modeling framework with a recently developed J₂-J₃ plasticity model for the matrix material. Model parameters are calibrated using experimental data, and the calibrated model predicts failure initiation and propagation in various specimens experiencing a wide range of triaxiality and Lode parameter combinations.

We develop and validate a computational reduced order mesoscale model (ROMM) to predict misfit dislocation structures of semi-coherent fcc/bcc interfaces. Our method employs anisotropic elasticity theory to calculate elastic energy of the interface and uses it as a tool to predict the dislocation patterns at the interface. We validated the predictions of our ROMM by comparing to disregistery analysis of atomistic simulations. The elastic energy calculations from our computational model are in quantitative agreement with atomistic interfacial energy calculations. Our ROMM can be used for designing semicoherent interfaces with tailored properties.

Integrated circuit packaging technology has become a prime design consideration for the development of electronic system concepts. One key issue is the bonding layer between chip and substrate. Currently, high-lead solder materials are being used, which apart from their environmental problem, limits the reliable operation temperature of devices to temperatures lower than 1750C. Low-temperature bonding (LTB) by nano-sized silver sintering is emerging as a promising replacement for making highly reliable power electronics modules working at elevated (250 0C) temperatures.
In this project, several thin (~25 µm) layers of porous nano-crystalline silver are produced by sintering nano-sized silver paste at reasonably low temperatures, pressures and times. The effects of the different sintering conditions on the microstructure and thermo-mechanical behavior of the sample are studied. The microstructure is characterized by electron microscopy, X-ray nano tomography and X-ray Ptychographic microscopy in terms of bulk porosity, grain size and defect structures such as twins and dislocations. We find that microstructure depends strongly on the sintering conditions.
The thermo-mechanical behaviour of the nano-silver layers is investigated by in-situ tensile testing at the Materials Science beamline of the Swiss Light Source (SLS). The samples exhibit a viscous behaviour and a strong strain rate sensitivity of the flow stress and elongation-to-failure.
In-situ (during X-ray diffraction) load-unload and stress relaxation tests at room and elevated temperatures are performed to study the deformation mechanisms. The evolution of the peak broadening provides information on the recovery mechanisms in the sample. A significant recovery of the peak broadening after unloading and during relaxation is observed. This may be related to the escape of dislocations at the free inner surfaces and/or grain boundaries.

Energy storage is a wide field of research in which porous materials can play a significant role. Some materials show specific hydrophobicity or flexibility properties that can be efficiently used for energy storage applications. Indeed, these systems can be imagined as nano-springs, nano-dampeners or nano-shock absorbers. The relevant properties can be investigated using thermomechanical methods such as water intrusion-extrusion (hydrophobic porous materials) or mechanical compression-decompression leading to high volume variation (flexible porous materials). However, the direct measurement of the energy dissipated is not trivial.
Our group has developed a specific set-up based on the possibility to force a fluid either to penetrate the porous structure or, for non-penetrating fluids, to compress it. In contrast to other set-ups the energy evolved is directly measured using calorimetry. Thus it is possible to simultaneously calculate the internal energy balance from the mechanical work involved and the measured heat.
Hydrophobic materials such as high-silica zeolites have been analysed by water intrusion. Microporous samples are interesting because the water intrusion occurs at high pressure and leads to high mechanical work. On the other hand, several metal-organic frameworks (MOFs) have been studied by compression. The flexibility (or “breathing”) of some MOFs is observed under mechanical stress. The energy involved in the structural transition between the large pore structure and the narrow pore one observed for MIL-53 materials has been evaluated [1]. To increase the allowable pressure, and consequently the possible storage of mechanical energy, more “rigid” structures such as MIL-47 have been also investigated. Different energy behaviours are shown and which opens up the above mentioned applications in mechanical storage of energy as molecular springs, shock absorbers or dampers.
This work was carried out in the framework of the French ANR project “MODS”

The mechanical behavior of nano-porous materials is characterized by non-linearity, hysteresis, anisotropy and susceptibility to fluid sorption. For instance, moisture adsorption induces swelling in cellulose and weakens its mechanical properties.
To understand and explain this complex behavior, a multi-scale "dependent domain" model is developed. At the nano-scale, a set of interacting constitutive elements are employed, which shows mechanical character (compression-shear) and reside in different moisture states and each state is defined by a set of internal forces acting on the element. When subjected to mechanical loading and/or moisture loading, the elements may change state (mechanical and/or moisture). The essential input to a description of these systems under loading is the set of equations which determine the evolution of these states with external loading. The changes of mechanical and moisture states are coupled. Different couplings describe the different behavior of nano-porous materials to sets of mechanical /moisture loading. Moisture influences the mechanical states by modifying the internal forces acting on a constitutive element and the mechanical stresses influence the moisture states by modifying the filling/emptying chemical potential. The evolution of mechanical and moisture states with loading can be modeled with the help of a model at a lower scale, which forms the next step of this model.
All of the well-known properties of porous materials of interest are able to be described by this model. The model is shown to perform well in modeling systems ranging from pure materials, granular media, and composite materials to hierarchical materials like wood.

Although the strength of periodic lattice materials has been widely investigated over the past two decades, most failure models have focused on the competition between yielding and buckling of the struts, with little attention to their fracture phenomena. The few existing fracture models of cellular materials treat the medium as a continuum, and assume the presence of pre-existing cracks that are long in comparison with the unit cell size. Although these models allow ready extraction of elegant scaling laws (and predict that the lattice toughness scales with the square root of the unit cell length), they cannot capture the effect of wall micro-cracks on the strength of otherwise perfect cellular materials. In this work, we investigate the effect of nodal micro-cracks on the compressive response of hollow microlattices, assuming that lattice failure results from the competition among plastic collapse, brittle fracture and local buckling of partially cracked lattice bars. This failure model is used to investigate the role of the constituent material toughness on the lattice strength and attempt to identify lattice topologies and geometries that minimize the effect of micro-cracks on failure.

Some of the best examples of composites with exceptional mechanical properties are natural hierarchical materials such as bone, wood, enamel, and shells. The high performance of these composites is attributed to structural design rules rather than to the individual materials, which are often quite weak or brittle, and to the fact that the structures are optimized for specific loading conditions. Many of the successful engineering approaches to designing high performance composites have been based on copying the hierarchical composite structures from Nature but resort to a broader palette of component materials to achieve even better mechanical performance. However, most natural and man-made composites are anisotropic, likely reflecting the difficulty of synthesizing fully three-dimensional structures, and thereby limiting their use under variable loading conditions.
In this study, we consider fully isotropic composites which are expected to show a more consistent response under different loading conditions than anisotropic structures. Specifically, we investigate the stiffness, strength, and toughness of nanoporous Au (cell sizes of order 100 nm) that has been infiltrated with various polymers. We compare the measured mechanical properties with predictions from finite element modeling based on the actual nanoscale composite structure that is obtained by focused ion beam serial sectioning. We find that the composite stiffness is in quantitative agreement with the moduli of the component materials in bulk form, whereas explaining the measured composite strength requires that the Au ligaments must reach flow stresses well above the bulk values. We propose that the strength of the ligaments is controlled by the nucleation of dislocations at the interfaces at stresses of order of 1 GPa. The fracture toughness of the composites can be understood in terms of a plastic zone size which is constrained by limited transmission of deformation across the interfaces. We argue that the interface adhesion between the Au ligaments and the polymer determines whether the composites fail by ductile or brittle fracture.

Colloidal nanomaterials with hierarchical structures show great potentials for applications such as catalysis, plasmonics, and biology; however, it is challenging to lower the interfacial energy between different materials to facilitate the overgrowth of hierarchical nanostructures. We report a concept, in which self-assembled surfactant molecules are introduced to integrate different materials into nanocomposite during the colloidal synthesis. Self-assembled cetyltrimethylammonium bromide (CTAB) molecules are used to guide the aligned overgrowth of various mesoporous and microporous materials on versatile nanocrystals to form well-defined core-shell structures. These hierarchical core-shell structures demonstrate a controlled encasement across a wide range of materials and the critical role of CTAB to manipulate the interfacial energy.
Note: This work is under minor revisions on J. Am. Chem. Soc.

Porous microcracked ceramics represent a unique material class widely used in thermal
management, power generation, and filtration applications. These materials have an
unusual nonlinear mechanical response that is contrary to the behavior of traditional
brittle fracture of other ceramics. The bulk processing affects the grain orientations and
porosity. The network of pores and microcracks leads to a heterogeneous structure with
unusual mechanical behavior. This work employs microscale uniaxial tension coupled with
digital image correlation to investigate anisotropy in the mechanical properties of
ceramics used in diesel particulate fuel filters. In probing these bulk mechanical
properties this work gains insight into the nonlinear response of microcracks in a porous
elastic medium.

Composite nanomaterials are attractive for many applications including catalysis, plasmonics, sensing, imaging, and biology. In such composite nanomaterials, it is desired, yet still challenging to have a controlled alignment at the interfaces between materials with lattice parameters in disparate scales. To address this challenge, we develop a new strategy of colloidal synthesis, in which self-assembled molecular layers are introduced to control the alignment between different materials. To demonstrate this concept, self-assembled cetyltrimethylammonium bromide (CTAB) self-assembled molecular layer is used to bridge interfaces in a core-shell nanocomposite with a well-defined metal nanocrystal core and a metal-organic-framework (MOF) shell, which differs in structural dimensions by orders of magnitude. We show that single metal nanocrystals are encased individually in single-crystalline MOFs and a controlled alignment between the crystal planes of the metal and MOF is observed.

Today, representative volume element (RVE) or unit cell (RUC) models are routinely employed for the estimation of mechanical properties of complex material microstructures. Numerous advances have appeared in the last 20 years for computational methods seeking to coarsen, homogenize, or statistically estimate properties in such models. Significant challenges now remain at the mesoscale where models are needed for semi-crystalline, percolated, or experimentally-determined structures and configurations. We present numerical evidence that direct application of existing numerical approaches may prove problematic.
In general, RVE discretized models must be refined so that the computed properties are converged in the sense of h-convergence. When the internal material interfaces in the simulated domain are of such random arrangements that small feature sizes exist, such as that may appear near a percolation threshold, the resulting modeling errors can make converged properties difficult to obtain. The microstructures may contain load bridges several orders of magnitude smaller than other more volumetrically-dominant morphological features in the unit cell.
In the talk, we report h-convergence rates, the microstructure models from which they are obtained, and the proposed explanation for why such surprisingly low convergence rates may be a general and possibly commonly-encountered result. The complexity of the microstructure is presently quantified by the number, length, and approximate radii of the load bridges. Through the study of a sequence of increasingly refined models, the convergence of elastic properties with respect to grid resolution of the computer models is determined. The rates are contrasted with those of simpler microstructures, namely polycrystals and unidirectional composites, for which traditional finite element error estimates apply. The numerical results show that microstructure complexity can drastically degrade the convergence of the homogenized properties and therefore may demand prohibitively large numbers of degrees of freedom to yield accurate solutions.

Nanoporous silver foams (75% porosity) synthesized by dealloying Ag₂₅Al₇₅ using two different electrolytes were heat treated in either argon or vacuum in order to induce changes in the morphology and ligament size. Several techniques including scanning electron microscopy, Raman spectroscopy, and X-ray powder diffraction are utilized to study the elevated temperature morphology and oxide formation. The ligament sizes increase with heat treating temperature, except for the sample heat treated in vacuum at 600 °C. Results show no significant silver oxide formation for any of the foams.

Because of the large surface-area-to-volume ratio that they exhibit, nanoporous metals offer exciting possibilities in various fields such as catalysis, sensing, MEMS and biomedical applications. However, when the cell size of porous metals is decreased to the nanoscale, samples become extremely brittle, in spite of the inherent ductility of metals. This represents a serious disadvantage for direct applications.
Bulk nanoporous gold (np-Au) samples were produced by dealloying of gold-silver alloys. A combination of free and electrochemical dealloying steps was used to obtain a crack-free structure without shrinking the sample. Removal of the sacrificial element (silver) and formation of the nanoporous structure were verified by scanning electron microscopy and energy dispersive x-ray spectroscopy. Mechanical properties of np-Au specimens with millimeter-scale dimensions were determined by tension and compression testing, and by nanoindentation. Observation of the fracture surface after mechanical testing revealed extensive plastic deformation and necking of the ligaments prior to rupture, despite the macroscopically brittle, catastrophic failure of the specimen.
In general, the relations linking the mechanical properties of porous metals to those of their fully dense counterparts do not take the pore cell size into consideration. As the mechanical properties of metals typically change when the sample size decreases to the nanoscale, scaling relations need to account for these size effects. Results of nanoindentation, tension and compression testing were used as the basis for proposing updated scaling relations that better describe the properties of nanoporous metals. Moreover, the new scaling relations incorporate results from studies of size effects in nanowire systems, and thus provide a bridge between these two material systems, for better understanding the mechanical behavior of nanoscale metals and alloys.

Spall failure of ductile materials during shock loading is the result of void nucleation, growth and subsequent coalescence into cracks. One proposed mechanism for void growth is the nucleation of dislocations from the void surface. Once nucleated, the dislocation expands as a shear loop on its glide plane. However, a shear loop by itself will only distort the void and will not cause its volume to change. For volume change to occur the dislocation shear loop must form a prismatic loop and detach from the void surface. This can take place through several cross-slip events of a single shear loop, a classical mechanism used to describe prismatic loop emission from precipitates. Alternatively, several shear loops can be nucleated simultaneously on different glide planes and merge to form the prismatic loop, a mechanism observed in atomistic simulations. The production of prismatic loops from a precipitate embedded in a metallic matrix also occurs through a similar process leading to decohesion of their interface and localized plastic hardening.
In the present work, we use a coupled discrete dislocation dynamics - finite element (DDD-FEM) code to model the evolution of dislocations nucleated from heterogeneities. Dislocations in an infinite bulk FCC crystal are modeled with the ParaDis DDD code and the correction fields produced by the heterogeneous material properties are determined with a parallel finite element code. The two codes are coupled through a scalable data transfer module allowing independent domain decomposition and computational resource allocation. We first report results for the evolution of a single shear dislocation nucleated from the surface of the void and show the steps leading to the formation of a single prismatic loop in FCC crystals. The alternative mechanism for the formation of prismatic loops through the simultaneous nucleation of shear dislocations loops from different glide planes is also considered. The active mechanism is shown to be dependent on the magnitude and direction of the far-field loading. A dislocation nucleation criterion is then implemented and the system is allowed to evolve under a quasi-static stress state leading to the emission of several prismatic loops whose number, spacing and nucleation rate is determined.

Nanoscale multilayered metal composites exhibit extraordinary strengths approaching a significant fraction of the theoretical strengths of the constituent metals, but the relationship between interface structure and the strengthening mechanisms remains not well-understood. In the study, we present the results of our recent molecular dynamics (MD) simulations on two types of nanolayer bi-metal composite structures: Cu/Ag and Cu/Al. While the interface structures of both these nanolayer composite structures are semi-coherent, they exhibit entirely different deformation behavior under out-of-plane tension. For Cu/Ag nanolayered metals, our MD simulations demonstrate that a novel interlayer interface migration mechanism is triggered at a critical tensile strain, which abruptly causes the initially planar Cu/Ag nanolayers to become wavy. This planar-to-wavy transition is facilitated by the low shear resistance of the Cu/Ag interlayer interface which slips to accommodate the out-of-plane deformation. High stress concentrations subsequently develop at the summits and valleys of the wavy Cu/Ag interlayer interfaces, from which micro-twinning partials are emitted. Thus the wavelength of the wavy Cu/Ag nanolayer structure forms a critical length-scale for the distribution of periodic defect sources for twin nucleation, and is responsible for the size-dependent strengthening of the Cu/Ag nanolayered metals. In contrast, the Cu/Al nanolayered metals remain planar throughout the deformation due to the high shear resistance of the interface. Instead, closed stacking fault tetrahedras (SFTs) develop along the Cu interlayers during the deformation process, and in turn trigger the formation of open SFTs in the Al interlayers. The formation of these SFTs is closely related to competing characteristic length-scales: interlayer thickness versus the size of the stacking faults along the interface. These results highlight the importance of the interface structure in controlling the deformation mechanisms, and can explain the interlayer-thickness dependent strengthening mechanisms for semi-coherent multilayered metals at the nanoscale.

Nanocrystalline materials exhibit high-strength characteristics primarily governed by statistical nature of nonlocal cooperative grain-boundary failure processes. As the grain size reduces, the strength increases until it drops at a nano scale due to small-length-scale cooperative mechanisms of deformation and failure. Here, we review recent advances in hybrid methods of experimental and numerical analyses for measuring the strength and fracture toughness of nanocrystalline materials associated with the cooperative failure processes. An approach is a hybrid method based on in situ TEM analysis of nano-scale failure processes and measurements of nano-scale crack-opening displacements, which are then used to estimate the fracture toughness by employing an inverse finite element analysis. The nominal yield strength, the nominal plastic hardening modulus are also determined by the inverse finite element method to match numerical crack opening profiles with the experimental counterpart. Another approach is composed of AFM interferometry and nonlinear filed projection analysis. The nonlinear field projection (NFP) method is implemented through interaction integrals, for inverse extractions of nonlocal-deformation near-fields of the failure process from the measured elastic far-fields. The nonlinear field projection method together with another interior field projection method bridges the information of the atomic scale nonlocal-deformation regions to experimentally measured continuum fields of the cooperative deformation and failure processes.

Cross slip is of fundamental importance for dislocation multiplication, strain hardening, fatigue and dynamic recovery processes. Atomistic and mesoscale computational models are combined to clarify the effect of cross slip on the stress-strain response of face-centered cubic (FCC) metals. The atomistic model is used to construct the energy barrier of cross slip as a function of multiple stress components. This leads to a prediction of cross slip rate as a function of the local stress, which is used as an input function to the mesoscale, dislocation dynamics (DD) model. The single-crystal stress-strain curves and dislocation microstructures predicted by DD simulations are compared to experiments, to elucidate the effect of cross slip. The algorithmic improvements that enable DD simulations to reach sufficient strain needed for such comparison are also discussed.

In recent years, our research group has formulated a new framework called Materials Knowledge Systems (MKS) for establishing highly accurate metamodels for localization (opposite of homogenization) linkages in hierarchical materials systems. These computationally efficient linkages are designed to capture accurately the microscale spatial distribution of a response field of interest in the representative volume element (RVE) of a material, when subjected to an imposed macroscale loading condition. In prior work, the viability and computational advantages of the MKS approach were demonstrated in a number of case studies involving multiphase composites, where the local material state in each spatial bin of the RVE was permitted to be any one of a limited number of material phases (i.e., restricted to a set of discrete local states of the material). In this study, we present a major extension to the MKS framework that allows a computationally efficient treatment of significantly more complex local states of the material. In this study, we present an important extension of the MKS approach that permits calibration of the influence kernels of the localization linkages for an entire class of low to moderate contrast material systems as opposed to the prior protocols that addressed one material system at a time. For high contrast single phase and multi-phase polycrystals, the MKS series include higher order terms. These major advances in the MKS framework are facilitated by the use of suitable Fourier representations of the influence functions. This paperdescribes this new formulation and the associated calibration protocols, and demonstrates its viability with case studies of different material systems.

Experimental results indicate that metallic multilayers have unusual properties such as high strength, measurable plasticity and high strain hardening rate when both layers are nanoscale. Both the yield strength and the strain hardening rate show a pronounced size effect, depending not only on the layer thickness but also on the layer thickness ratio. The strain hardening behavior of metallic multilayers was analyzed using a three-dimensional crystal elastic-plastic model (3DCEPM) that describes plastic deformation based on the evolution of dislocation density in the constituent layers according to confined layer slip mechanism. These glide dislocations nucleate at interfaces, glide inside layers and are deposited at interfaces that impede slip transmission. The unusually high strain hardening rate, approaching 50% of the Young&’s modulus, is ascribed to the closely spaced dislocation arrays deposited at interfaces and the load transfer that is related to the layer thickness ratio of the constituent layers. This research is sponsored by DOE, Office of Science, Office of Basic Energy Sciences.

Nanoporous silicon (np-Si) is an attractive potential anode material for lithium ion batteries, as it offers a large amount of free volume for lithium insertion and de-insertion, allowing the anode to swell and contract without cracking during lithium cycling. Understanding the mechanical behavior of np-Si is challenging, as the nanoscale ligaments (20 nm wide) induce size effects and can change the fundamental deformation mechanism(s) in Si at this length scale. High-purity (100% Si content) np-Si was fabricated by dealloying precursor materials, and the mechanical behavior was measured for these specimens. In-situ nanoindentation in the TEM, performed on as-dealloyed thin film np-Si, revealed that this material can withstand extensive deformation without exhibiting brittle fracture. After significant compression under the indenter tip, np-Si fully recovered this deformation and the ligaments returned to their original configuration. Additionally, ex-situ nanoindentation was performed on np-Si, to better understand the mechanical response of this material and determine if residual deformation could be induced. When indented to a sufficient depth, np-Si did experience permanent deformation, although the Si ligaments did not fail in a brittle manner. This behavior will be discussed in the context of size effects on the plastic deformation behavior of nanoscale Si, including ductile versus brittle deformation of Si ligaments.

Material defects alter the evolution of dislocations by directly impeding motion and perturbing the homogenous elastic fields of the bulk crystal. The small scale plasticity occurring in the vicinity of crystal defects is dependent on the motion of individual dislocations and is therefore well suited for discrete dislocation dynamics (DDD) methods where plasticity is explicitly captured by the motion of dislocations. In the last two decades, multiple analytical and numerical methods have been developed in attempt to incorporate the complex stress fields due to microstructure and free surface effects. However, modeling realistic length scales, time scales, and microstructure has shown to be intractable with current DDD algorithms. In this work, we develop a scalable algorithm for modeling DDD with microstructural effects. The method involves coupling a highly parallel DDD simulator for bulk materials (ParaDiS) with a highly parallel finite element method (FEM) solver to capture microstructual effects. Using a scalable data transfer algorithm, we are able to independently control the domain decomposition and computational resource allocation of each application to enable orders of magnitude increases in tractable system sizes.
In the present work we use the DDD-FEM code to simulate dislocations interacting with inhomogeneities in three dimensions. Paradis allows us to model high dislocation densities in 3D while the parallel FE code enables the simulation of large domains containing finely resolved inhomogeneities. We have also introduced a stress based dislocation nucleation criterion to allow for nucleation events due to stress concentrations created by voids and precipitates. From these simulations of metals containing voids and precipitates we determine the strain hardening mechanisms associated with dislocation nucleation, void strengthening, Orowan looping, and forest hardening. These simulations elucidate the role of inhomogeneity shape, size and density on strain hardening mechanisms.