Engineered open-cell foams offer a myriad of choices in material, pore size, porosity, cell structure, density, strength and processing method that enable the material to be optimized for many demanding applications.
Engineered advanced material foams are used as filters, lightweight structures, insulation, kiln furniture, heat exchangers, catalytic converters, orthopedic implants and many other applications because they offer so many choices in performance capabilities. This presentation will review how design choices interact to determine the properties of the resulting cellular material. Examples of engineered advanced material foam and composite structures built from this designed cellular material will be discussed.

There are two major properties determining the suitability of a material for lightweight applications, the material strength and the material stiffness. Technical foams are porous solids having extremely low densities. However, due to their stochastic architecture they only achieve limited values of specific strength and stiffness, typically well below those of corresponding bulk materials. For cellular materials, the quality of the architecture strongly affects the macroscopic material properties. Structural strength and stiffness have to be considered since stability problems and inhomogeneous stress distributions occur. Reaching extremely small scales, structural characteristics and material properties mutually depend on each other. Brittle materials become less sensitive to flaws, thus their strength is increasing and may even reach values close to the theoretical strength.
It is the aim of this work to take advantage of such size effects and create highly ordered hierarchical cellular materials with optimized topologies. Due to the length scale of architecture, material thicknesses thin enough to meet the corresponding length scale without affecting structural stability are achievable. Direct laser writing is applied to produce polymeric structures of true three-dimensional microarchitecture with design control down to the nanoscale. Using atomic layer deposition ceramic and composite designs are fabricated.
Several cellular materials of different truss or shell architecture were designed, manufactured and mechanically characterized. These materials have exceptional high macroscopic strength over density ratios compared to other cellular materials. Overall, it is found that shell constructions typically surpass open cellular designs. In summary, we demonstrate that the specific strength of our materials is in the range of technical ceramics and high strength steels.

Biomaterials such as bone and tooth achieve precisely tuned mechanical and interfacial properties by varying the concentration and orientation of their nanoscale constituents. However, the realization of such tunability in engineered foams is limited by manufacturing-driven tradeoffs among the size, order, and dispersion uniformity of the constituent building blocks. We demonstrate a scalable means of manufacturing nanocomposite foams comprising aligned carbon nanotubes (CNTs) conformally coated with ceramic by atomic layer deposition (ALD). By varying the coating thickness, we realize predictable ~1000-fold tuning of Young&’s modulus (14 MPa to 20 GPa), ultimate compressive strength (0.8 MPa to 0.16 GPa), and energy absorption (0.4 to 400 J/cm³). The compressive strength of the core-shell nanofoam is 10-fold greater than commercially available aluminum foam over the same density range, and the compressive stiffness and strength equal that of compact bone at 10% lower density. Moreover, this material presents a highly efficient design for energy absorption because the nanoscale members are weakly interacting beams rather than interconnected webs as in conventional open-cell foams. Coated CNT foams may enable new materials for mechanical and multifunctional applications such as catalysis, filtration, and thermal protection.
A. Brieland-Shoultz, S. Tawfick and S.J. Park contributed equally to this manuscript.

The specific strength of a cellular material is governed by that of the materials used to make it, the volume fraction of the cellular solid occupied by this material, and the cell topology. Cell topologies that are stretch dominated, and whose inter cell nodes do not rotate during loading are in general stronger (and stiffer) than in which the cell members bend. Bounding theorems govern the upper limit of attainable strength in a strength-density material property space, and cells with lattice truss or square honeycomb topologies come closest to attaining these bounds. The octet truss lattice also offers the sometimes useful advantage of near isotropic strength under multi-axial loading conditions. The use of small diameter lattice trusses also opens up opportunities to exploit microscale strengthening mechanisms that are difficult to implement in monolithic materials. This talk will describe recent efforts to exploit these design principles to make new cellular materials with engineering alloy-like strengths, but with densities well below those of water.

Hollow microlattices with periodic cellular architecture are fabricated by depositing various thin films materials (Au, Cu, Ni, SiO2, poly(C8H4F4)) onto sacrificial polymer lattice templates. Densities from 0.5 mg/cm3 to 500 mg/cm3 are achieved and the density scaling of Young&’s modulus and strength are determined. At low relative densities, recovery from compressive strains of 50% and higher is observed, independent of lattice material and predictable by an analytical model. At higher densities the crushing performance can be tailored by modifying the cellular architecture to achieve energy absorption properties of interest for protection applications.

A novel method for fabricating hybrid carbon fiber hybrid structures has been developed. This involves the use of high performance polymer and syntactic foam materials as mold shaped space holders, Hexcel IM7 carbon fiber tows, braids, and pultruded rods as the trusses, and subsequent infusion with resin, using a vacuum assisted resin transfer molding (VaRTM) process. This talk would describe the fabrication process in detail for both octet and pyramidal lattices, as well as the measured mechanical properties of these structures. The talk would also examine how these mechanical properties compare to those of current leading high performance materials in terms of compressive strength, modulus, and energy absorption.

Shock compression produces states at elevated pressure, temperature and strain rate, conditions conducive to chemical reaction in most organic (predominantly C, H, N, O-based) materials. Similarly to high explosives, polymers and foams decompose at shock pressures above some threshold on their principal Hugoniot (shock adiabat), with its precise location being dictated by the details of chemical and microstructure. Failure to capture these transformations results in significant loss of information regarding pressure-volume-temperature pathways followed by materials under shock (hydrodynamic) conditions. This presentation will provide an introduction to shock-induced chemistry, examining in detail its signatures and consequences in polyurethane foam as an example. A novel target configuration was developed to obtain Hugoniot points for up to 4 foam samples in a single gas-gun experiment, facilitating collection of over 20 new points at a range of initial densities; in this manner we were able to address a gap in previous literature. Polyurethane of moderate porosity was found to exhibit anomalous shock compression behavior, i.e., an increase in shock pressure lead to an increase in final volume. Thermodynamically complete inert and product equations of state were developed for polyurethane at full density, and a P-α compaction model was used to adjust the former to porous data. The product equation of state was based on the assumption of full thermodynamic and chemical equilibrium, a methodology commonly applied to high explosives. From this analysis it was determined that the shock-induced reaction threshold decreased from roughly 22 GPa to 1 GPa as the porosity increased from 0 to 70%, and states that appeared anomalous matched well those predicted by the product equation of state. Extension of shock compression techniques to novel structured foams, fabricated using optical waveguide techniques, will also be presented. A novel application of time-resolved x-ray phase contrast imaging to shock propagation in the structured foams has revealed the micron-level response of the foam struts under shock loading for the first time.

Poly(urethane) (PU) foams are ubiquitous in our modern society as a packing and filler material. They are a light-weight, hard foam that can be molded, or machined into many shapes for a wide variety of applications. These applications include structural components, base materials, typically with softer foam on top, or as a small ‘chunk&’ packing material. The primary goal of the study is to compare the foam structure between a molded part and a test block to determine the test blocks suitability for use as a surrogate for mechanical and dynamic testing. The molded piece has the shape of a cylindrical ring, tapered from one end to the other, whereas the test block is simply a solid rectangular piece. As a follow on project, it is important to determine the aging characteristics of polyurethane foam parts with respect to dimensional stability and mechanical properties. The chemistry of polyurethane foam production is dominated by three relatively simple chemical reactions. The first reaction of an isocyanate moiety with water leading to the formation of a carbamic acid intermediate. Carbamic acids are very unstable and decompose spontaneously to amines with evolution of carbon dioxide gas. Hence, this two-step reaction is responsible for the generation of gas in water blown polyurethane foams such as BKC 44306-10. It is the most exothermic of the reactions involved in polyurethane foam production and occurs with or without the addition of a catalyst. This blowing process creates a flow of material when filling a mold shape that can be imaged.
Three dimensional micro X-ray computed tomography (µCT) imaging is a powerful tool for the examination of the internal structures of polymer foams and other materials. When coupled with an image analysis package, X-ray µCT data provides quantitative information on the size, shape, and distribution of voids. In this study, we compare the void morphology in a molded piece of PU foam to those in a rectangular test block. From the molded piece and the test block, we cored cylinders of material and find even within the test block, there is a decrease in percent void volume (%Vv) and decrease in average void size when measured from the bulk to the skin, meaning that the material becomes more dense. The same set of measures on the molded part finds the same bulk-surface %Vv trends but also that there are highly eccentric voids existing near the surface due to high lamellar shear flow as well as increasing average void size further ‘up&’ the mold due to increased time progression. Interestingly, in thinner regions of the molded part, the equilibrium density is never reached and the voids become larger up the length of the part, leading to the conclusion that ~40 of the length of the part is outside of the density specification. Coupling µCT small regions of the foam parts with an in-situ load cell indicates that the load response and damage is highly dependent upon the cell morphology.

This work examines the synthesis and reaction mechanism of particle composite thermites. Direct ink writing (DIW) is used to prepare fine-featured conductive substrates, and electrophoretic deposition (EPD) is then used to deposit thin films of well-mixed thermites onto the substrates. A variety of electrode designs are investigated; both to explore the versatility of this combination of techniques, as well as to probe the reaction mechanism. Specifically, we find that the gas-trapping and degree of confinement can play a large role on the reactivity by impacting the forward energy transport of intermediate gases and particles. A nano-Al / nano-CuO thermite has been shown to exhibit over two orders of magnitude in propagation velocity by changing the confinement.

This poster will describe the characterization of fusion target materials using several unique X-ray methodologies. These laboratory-based techniques include; micro- and nano-scale X-ray tomography, confocal micro X-ray fluorescence (MXRF), and monochromatic radiography. With these techniques we can non-destructively image, both on the micro- and nano-scale, at high resolution, and measure densities and elemental compositions (potassium and above).
Metal-doped polymer capsules are composed of a 41 µm thick polymer shell, doped with 1.5 atomic weight percent gallium and germanium in 2 µm thick dopant regions. To gain an understanding of the elemental composition within the capsule as a function of theta, as well as capsule-to-capsule variations, confocal MXRF is used to measure the elemental profile (with ~30 µm resolution) through the shell thickness. These layers are directly imaged in 3D with nano-CT, up to 150 nm resolution.
The characterization of low density materials aerogels and polymer foams continues to be a topic of great interest. Here we present the use of X-ray scatter using confocal MXRF as well as monochromatic radiography using instrumentation based upon a concave germanium crystal optic and X-ray camera. With this instrumentation and the knowledge of the sample opacity from X-ray tables, it is possible to image material density variations (+/- 1%) in 2D as well as image higher density surface ‘skins&’.

The ability to pattern complex materials with high-speed and low-cost three-dimensional (3D) printing techniques is highly desirable. Here, we present recent progress on developing siloxane-based feedstock formulations, known as “inks,” for a unique 3D printing approach called Direct Ink Writing (DIW). DIW is a low-cost, mask-less printing route that enables rapid design and patterning of planar and three-dimensional (3D) microstructures. In this filamentary printing approach, a concentrated ink with tailored viscoelastic properties is deposited through a micro-nozzle that is translated using a multi-axis positioning stage. The ink rapidly solidifies as it is extruded so that 3D structures with fine features may be built up in a layer-by-layer fashion. We describe our work on developing novel ink materials with appropriate rheological properties that make them well-suited to our 3D printing approach. Next, we introduce the concept of tailoring the macro-scale mechanical properties by designing the 3D micro-architecture of the printed cellular silicone materials. We show the ability to obtain highly uniform or graded properties by simply adjusting the pattern design. Moreover, by understanding the materials-structure-processing property relationships, we have created a modeling-design-fabrication approach to achieve tailored mechanical properties. For example, we have created foam structures that, in one case, are well suited for pure compression and, in a separate case, are better suited for shear environments. We expect that the ability to deterministically program mechanical performance from part-to-part and within a part will prove useful for many applications that require energy absorption and dissipation.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. IM release number LLNL-ABS-639573.

Here, we exploited recent achievements in digital manufacturing, specifically multimaterial 3D printing, to advance a new paradigm of printed active composites (PACs). 3D printing opens additional design freedom to create composites with complex and controllable anisotropic thermomechanical behavior via the prescribed fiber architecture, shape, size, orientation and even spatial variation of these parameters. We directly printed a fibrous material from a CAD file that precisely specifies the fiber architecture at the lamina and laminate level. Our PACs are soft composites consisting of glassy polymer fibers reinforcing an elastomeric matrix. The glassy polymer fibers exhibit the shape memory effect and we used this to create active soft composites where the glassy polymer fibers serve as a switch to affect shape memory behavior of the composite. This allows us to create soft materials with shape memory behavior via the tailored fiber architecture as opposed to the complex chemistry of typical shape memory polymers. We imbued the active composites with intelligence, programmed into them via the lamina and laminate architecture and the thermomechanical training process that can be used to create active components with various functionalities via configurational changes. We demonstrated the realizations of this concept by printing flat lamina with prescribed fiber volume fractions and orientations. The lamina demonstrated anisotropic shape memory behavior which is described reasonably well by a nonlinear continuum theory that can be used to guide the design of PACs. We then designed and printed laminates in thin plate form that can then be thermomechanically programmed to assume complex three-dimensional configurations including bent, coiled, and twisted strips, folded shapes, and complex contoured shapes with nonuniform, spatially-varying curvature. The key here is that the 3D shape is obtained by the programmed workings of the active composite microstructure, not by a complex molding or forming process. We also showed how the printed active composites can be directly integrated with other printed functionalities to create devices; here we demonstrate this by creating a box that can assemble itself via PAC hinges.
With the advancement of additive manufacturing, we believe our approach represents a new paradigm in designing, creating, and manufacturing of emerging field of printing active composites.

Aerogels are typically micro- and mesoporous (pores <300 nm), ultra-lighweight materials that can achieve surface areas in excess of 3000 m^2/g. As such, they are used in a wide range of applications ranging including catalysts and catalyst supports, energy storage and conversion, thermal and acoustic insulation, and sorbents for water purification. Aerogels are made via the sol-gel process, in which a reaction solution is gelled and the solvent is extracted in such a way as to leave the porous solid matrix intact. Though their pore sizes can typically be tuned by varying the synthetic parameters of the sol-gel process, limitations do exist. For applications that require faster mass transport through the aerogel, alternative methods for incorporating larger pore networks into the aerogel structure are desired. Herein, we report the development of direct ink writing (DIW) sol-gel materials, which upon drying become DIW aerogels. Characterization of the DIW aerogels will be discussed in comparison to their bulk counterparts.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the DOE Office of Energy Efficiency and Renewable Energy.

Electrophoretic deposition (EPD) is an industrially relevant process in which colloidal particles are suspended in a liquid migrate to and deposit on an electrode under an applied electric field. EPD has generally been limited to the fabrication of materials with gradients in material properties normal to the electrode's surface (z-direction) due to the static nature of the electrode. Here, we present a novel EPD technique, light directed EPD, which utilizes a photoconductive electrode that can be dynamically patterned with light during the course of the deposition. This allows for the fabrication of graded materials in the x-,y-, and z axes. We present experimental results demonstrating the technique as well as numerical modeling of the deposition process on photoconductive electrodes.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

We report on the synthesis and mechanical behavior of nanocrystalline nanoporous (NP) metals with struts that are in the 4 - 40 nm range. Their hardness as assessed by nanoindentation is found to be in the range of 1-2 GPa. We attribute this enhancement in part due to geometry but also to the nanocrystalline nature of the struts. We synthesize NP metals with hierarchical geometrical features using such techniques as e-beam lithography that further enhance the foam properties.

The carbon foam formed by carbon nanotubes (CNTs) and graphene can derive many of functions from both nanostructure and microstructure and, as a result, can have better performance than other types of carbon foams. There are various approaches for producing CNT foam and CNT/graphene foam, including freeze drying, critical-point-drying, electrospun, directly forming during CNT synthesis process, etc. However, these approaches cannot fabricate the carbon foams with controllable engineered porosities. We developed a simple and scalable process to fabricate the CNT/graphene hybrid foams. We are able to control foam architecture (pore morphology, pore volume, and their distribution) and tune the morphology systematically. We achieved these by utilizing two different polymers. One is pyrolytic polymer for creating pores with designed shape, volume, and distribution. Another polymer is polyacrylonitrile, which is carbonized to form graphene features among CNTs. The fabricated CNT/graphene foams have high surface area and low density. They are elastic and conductive. The mechanical properties of the foams are related with the weight ratio of CNTs to polymers and the foam structures. The detail process and foam properties will be presented.

Recent progress in advanced manufacturing enables fabrication of macro-scale hollow metallic lattices with unit cells in the millimeter range and sub-unit cell features at the submicron scale, thus yielding a topologically architected cellular material with structural hierarchy spanning six orders of magnitude in length scale. If designed to minimize mass, these metallic microlattices can be manufactured with densities lower than 1mg/cm3. Upon uniaxial compression, these ultralight architected materials exhibit elastic recovery (20-50%) and damping capacity (psi;~0.15) unprecedented for any metallic system. If the density is increased, these effects subside, and the classic irreversible plastic collapse of cellular metals is recovered (generally resulting in high specific stiffness and strength). A full understanding of the effect of the lattice architecture on the mechanical behavior is essential to fully exploit the potential of these novel materials. This talk will discuss these architecture/properties relations and present analytical and numerical strategies for the optimal design of hollow microlattices. In particular, designs that maximize specific stiffness, specific strength, damping coefficient and combinations thereof will be identified. Based on the understanding of deformation and failure mechanisms in hollow microlattices, general concepts for the design of optimal materials architectures will be presented.

Freeze-casting is a method that has been widely used in biomaterials engineering to generate tunable, interconnected, macroporous structures. By exploiting the phase separation accompanying the freezing of a colloidal suspension, it is possible to create intricate 3D networks of polymers, ceramics, biomolecules, and composites. We have developed a method to freeze-cast PEDOT:PSS suspensions that can be applied to create 3D monoliths and films as thin as 300 nm. The resulting porosity and microstructure is dependent on freezing conditions and polymer concentration. For monoliths, the geometry and composition of the freeze-casting mold also affects the resulting porosity by affecting the nucleation and growth of ice crystals in the medium. We have observed tunable elastic modulus of the monoliths in compression via the incorporation of glycidoxypropyltrimethoxysilane (GOPS) in the suspension prior to freezing. Additionally, the incorporation of GOPS into the structure greatly improves monolith stability in hydrous systems. We have also observed that, while PEDOT:PSS is strongly hydrophilic, the wetting behavior of monoliths are dependent on surface pore size and orientation. Recently, we have developed a method for the freeze-casting of macroporous PEDOT:PSS thin films with tunable thickness and porosity. This method has also been applied to systems of TiO2 nanoparticles to create porous thin films, and is noteworthy since we are able to achieve nanometer-scale thicknesses with microstructure consistent with much thicker freeze-cast films.

Over the last few years, we have been developing a new photopolymerization process to create microlattice materials with lattice-based features ranging from tens of microns to millimeters. These materials are formed by interconnecting a three-dimensional array of self-propagating photopolymer waveguides, where each waveguide represents a single lattice member. Because the waveguides propagate from a single exposure plane and can be formed simultaneously, thick (> 1 in. possible) three-dimensional polymer microlattice materials can be formed in less than one minute. The inherent flexibility of this new approach enables precise control of the microlattice material architecture, which ultimately enables the design of a material to achieve a particular property or function. In this talk, I will give a brief overview on the current state of development and highlight some of our on-going research and commercialization efforts.

Complex, three-dimensional lightweight cellular materials inspired by nature, such as honeycomb and foam-like structures are desirable for a broad array of applications such as structural components, catalysts supports and energy efficient materials. However, they are extremely difficult to fabricate with the current state-of-the-art fabrication techniques. This paper reports the fabrication of complex, three-dimensional cellular materials with nanoscale features using a novel additive manufacturing approach, namely Projection Microstereolithography (PuSL). We demonstrate the utility of the system by producing a variety of microstructures with complex geometries and explored the potential of using the system to build meso-scale structures with micro-scale architecture and nano-scale features. These achievements pave the way for large scale micro- and nano- manufacturing that extends the current state-of-the-art of three-dimensional fabrication technologies.
The octet truss material, which will be demonstrated in this paper, with its micro-struts carrying tension or compression when loaded, is expected to have superior mechanical performance under compression as compared to regular engineering foams and natural scholastic foams at the same relative density. Our proof-of-concept results demonstrate superior compressive stiffness when compared to a tetrakaidecahedral cellular material architecture of the same density.

Ordered cellular solids have been reported to have more robust mechanical properties, in terms of compressive yield strength and stiffness, compared to stochastic foams. These mechanical properties are dependentdepend on relative density and follow scaling laws based on the deformation mechanism of the structure. The stiffness and yield strength of stretching-dominated structures, like the octet lattice, scale linearly with relative density, ρ; those of bending-dominated ones, i.e. stochastic foams, scale with ρ² and ρ^(3/2), respectively. Based on these scaling laws, the stiffness and strength of a low-density material can be improved by controlling the deformation mechanism of the structure itself.
We present the fabrication and compression of ultra-lightweight hollow cellular structures with different geometries and deformation modes created using two-photon lithography. The structures studied are on the order of 50mu;m or larger and are comprised of unit cells on the order of 10mu;m. The members that make up the unit cell are hollow elliptical tubes with a major axis on the order of 1mu;m and a wall thickness on the order of 100nm. The metallic coating, which comprises the lattice, is nanocrystalline Au with a grain size of 20-50nm. The ability to control the structural geometry on length scales down to nanometers allows provides an opportunityies to take advantage of the strengthening size effect previously observed in nanoscale metals. The multi-dimensional nature of these lattices provides lendsenables them to be (or something) an ideal platform to study and enhance mechanical properties via the combined effects of both structural and material responses.
In-situ uUniaxial compression experiments on nanolattices designed to deform by (1) bending, (2) stretching, and (3) stretching-periodic bending mechanisms were conducted in an in-situ nanomechanical instrument, InSEM, at a strain rate of 0.01 s-1 to strains of 60% and higher. Differences in deformation mode, strength, and ability to absorb energy are discussed in the framework of cellular solid deformation and nanomaterial-induced size effects.

Nanoporous Cu, Ag, and Pd foams (65-80% porous) were synthesized by dealloying processes. The pore and ligament size, ranging from 20 to 115 nm, can be controlled by either the dealloying process or the selection of electrolytes. The hardness values of the foams were measured by nanoindentation and micro Vickers hardness testing. The results, along with previous data for nanoporous Au, were compared to several predictions for foam deformation models, including modified elastic buckling and plastic collapse models. Overall, the hardness values of the nanoporous metal foams appear to follow the plastic collapse model.

The major scientific challenge in high-performance structural materials is the development of new stronger, tougher, and lightweight materials to support advances in diverse fields such as aerospace, transportation, and energy. One approach to improve performance is to mimic and replicate natural biological designs that exhibit unique damage-tolerance properties. Here, we report on our recent efforts to fabricate innovative laminated composites with a distinctive micro-architecture inspired by the mantis shrimp. We employ direct ink writing to create ceramic helicoidal lattice structures that are infiltrated with polymer. This helicoidal structure is one of the unique and prevailing patterns observed in exoskeletons in a large number of species of the arthropod phylum, primarily due to its fracture toughness. Each layer of the helicoidal structure is composed of parallel arrays of filaments embedded in a matrix material. The individual layers stack successively on each other, with each layer rotating by a small angle about its normal direction relative to the adjacent layer. We demonstrate that this design concept can be applied to conventional ceramic and polymeric materials, such as alumina and poly(methyl methacrylate) (PMMA) to create composites that display exceptional strength and toughness. Selected materials properties (e.g., Young&’s modulus, flexural and fracture properties) were evaluated through appropriate ASTM tests and laminated composites theory. Structure post-damage behavior was also investigated. Significant improvement in the mechanical performance of the bio-inspired structure was observed over the baseline structure. Moreover, this additive manufacturing approach is flexible and can be readily extended to other material combinations and bio-inspired designs.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Release number: LLNL-ABS-639576

While the effect of deformation on the mechanical attributes, such as energy absorption, stiffness and thermal properties of cellular materials have been widely investigated, there have been few attempts to test whether the large deformation of these structures may be used to systematically achieve additional functionalities. Here, I will show that highly deformable cellular structures are excellent candidates to design a new class of responsive devices. Although instabilities have traditionally been viewed as an inconvenience, I will show that they can be exploited to create materials with novel and switchable functionalities. Possible and exciting applications include materials with unusual properties such negative Poisson&’s ratio, phononic crystals with tunable low-frequency acoustic band gaps, reversible encapsulation systems and systems capable of spontaneously switching between achiral and chiral configurations.

Cellular materials are not only characterized by outstanding mechanical properties, but they can also exhibit dramatic changes in architecture in response to external stimuli. Beyond the instability threshold, significant changes of the structures occur and the interconnectivity of the structures allows an effective interaction with neighboring cells, thus potentially yielding uniformly patterned structures. For elastic materials, the process is reversible and it occurs over a narrow range of the applied load, so that it can be exploited to design materials with switchable functionalities. As a result, there has been growing interest in investigating the the large deformation behavior of cellular systems as well as to harness the phenomenon.
We have studied complex patterns generated from geometrically frustrated cellular structures where a local order preferred by neighboring cell wall interactions cannot propagate through the entire cellular structures due to geometrical constraints. Using analytical, numerical, and experimental methods, we will present how ordered patterns can form in this system by geometrical instabilities. Our findings will not only enhance our understanding about fundamental principles that govern the behaviors of cellular materials structures, but also can find potential applications in controlling mass flow and wave propagation.

Recent advances in the mathematical formulations for structural design optimization
using the level set methodology have enhanced the treatment of a key feature introduced and typically ignored in multi-phase optimization models: solid interfaces. Material interfaces play a pivotal role in the actual performance of a structure, often dictating lifetime and failure characteristics, tolerances and processing choices. The motivation of the present study is to highlight the influence of interface properties, arising from microstructural factors, on the optimal design of structures. The methodology accounts for a nite and physically-motivated interface zone, in contrast to mathematically sharp and ideal interface surfaces. Over this interface zone, the material properties are considered to be graded, varying either monotonically or non-monotonically between disparate bulk properties. Several benchmark elastic and thermoelastic engineering problems involving structural compliance or displacement minimization are used to demonstrate signicant performance changes that are linked to local interface properties.

Recent advances in topological optimization methodologies for design of internal material architecture, coupled with the emergence of micro- and nanoscale fabrication processes, 3D imaging, and nanoscale testing methodologies, now make it possible to design, fabricate, and characterize structural materials with unprecedented control. This talk will describe a collaborative effort linking computational optimization with scalable 3D braiding and weaving technologies to design and fabricate lattice materials with high permeability and stiffness. Optimization of lattice architectures includes: volume fraction, wire type and placement, wire geometry, and wire orientation. Vapor phase processing after textile manufacturing provides a route to advanced engineering alloys, e.g. the transformation of pure Ni wires to Ni-base superalloys with superior elevated temperature properties and colossal carburization that dramatically improves corrosion resistance. Once optimized and fabricated, these lattice materials must be characterized on all levels. Specialized techniques for characterizing the resulting 3D structures and properties will also be discussed.

The aim of this research is to introduce analytical tools that enable the rapid optimization of general microstructural architectures that consist of truss-like beam-elements joined together in a lattice of repeating unit cells. Using these tools, designers may efficiently tune the material properties and geometric parameters of individual beam-elements within the lattice to create a design that most closely achieves a desired set of bulk thermal and mechanical target properties. Examples of such properties include thermal expansion, thermal conductivity, Young&’s modulus, yield strength, and density. The optimization tools presented here are complementary to the Freedom and Constraint Topologies (FACT) synthesis approach in that they are customized for optimizing the various “starting-point” topologies that designers are guaranteed to generate using FACT&’s comprehensive library of geometric shapes.
As most microstructural architectures possess a complex network of differently-sized interconnecting beams and some of the aforementioned bulk properties depend on how many unit cells constitute the overall lattice, most Finite Element Methods (FEM) are not capable of meshing such architectures let alone optimizing their many parameters. Moreover, the analysis and optimization speeds with which FEM or other numerical approaches (e.g., topology optimization) operate are much less than the speeds that the closed-form equations introduced here are capable of achieving. Although others have developed analytical tools for calculating some of the previously proposed properties for specific lattice designs, general analytical tools for simultaneously calculating all of the proposed properties for the complete body of designs that consist of multi-material beam-elements has not been proposed prior to this work. Such tools would greatly impact the design of new materials that achieve unprecedented property requirements for many advanced applications (e.g., light-weight, high-strength materials intended for mounting precision optics within a laser range finder on board a jet that undergoes large changes in speed and temperature during flight).
As a case study, we use the tools introduced here to optimize the bulk properties of a FACT-designed microstructural architecture that can achieve zero or negative thermal expansions. We use these analytical tools to generate four Ashby plots (i.e., expansion vs. modulus, expansion vs. conductivity, modulus vs. strength, and modulus vs. density) to compare this architecture&’s range of possible properties with those of naturally occurring materials. Experimental validation and finite element verification are also provided to demonstrate the accuracy of the tools provided.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-639379.

3D scaffolds have been frequently used not only in creating normal healthy tissue for tissue repair but also in creating in vitro disease models for drug screening. Recently, the importance of culturing cells in 3D has been recognized. It has been shown that cells cultured in 3D scaffolds show different growth profile and protein expression characteristics than those cultured in 2D. In addition, 3D scaffolds also have been frequently used as surgical implants, such as bone implants and cardiovascular stents.
There are two major types of scaffolds, i.e. scaffolds with a range of irregular pore sizes and those with well controlled regular pore size such as the scaffolds produced from 3D fabrication technology. It is well known that porous structure of the scaffolds, such as the pore size and porosity, affects not only the mechanical properties, but also the cellular response of the scaffolds. Therefore, a 3D fabrication technology that can produce scaffolds with well controlled porous structure is needed.
At 3D Biotek, we have developed various 3D scaffolds with engineered porous structure designs for various biomedical applications, ranging from 3D in vitro models for drug screening to bone and cardiovascular implants. This presentation will summarize our research results in these areas. .
Acknowledgement: Multiple grants from NIH SBIR Grants # 1R43HL114159 - 01, 1 R43 RR028022-01, and New Jersey Edison Innovative R&D Grant # 08-2042-014-25 are greatly appreciated.

Organic composite materials can be readily found in our daily life, such as plywood used in construction industry and bamboo composites as indoor and outdoor flooring materials. These organic composite material systems consist of cellulose fibers bonded with each other through an adhesive, leading to a bonded system with a gradient structure that possesses a unique structural behavior which has a great potential to be used as load-bearing building materials. In view of the manufacturing process of such composite material systems and the structure in-between the cellulose fibers and the adhesive, the interfacial adhesion of such systems at multiscale would play a major role in determining their capability in load-bearing structural applications. In this research work, the interaction between cellulose fibers and phenol-formaldehyde (adhesive) is chosen as a representative of the organic composite material system and molecular dynamics simulation is used for quantifying the corresponding interfacial adhesion. Here we demonstrate that cellulose fibers have a strong affinity to a phenol-formaldehyde surface with an interfacial strength of several hundreds of thousand N/cm2. The mechanism of such strong adhesion is a formation of hydrogen bonding between the cellulose and the adhesive. However, it is observed that the adhesion will be weakened in the presence of water, and hence the long performance and durability of such organic composite materials should be considered when such systems are present in civil infrastructures.

316L stainless steel, cobalt chromium alloys, and titanium-based alloys are common materials for hip replacement implants. They are generally used in current hip prostheses as either fully-dense or composite, or porous-coating. Although successful with respect to implant fixation, existing prostheses have mechanical properties that do not match those of the surrounding bone. Lack of mechanical biocompatibility yields stress shielding, with consequent loss of femoral bone stock. Bone resorption is ubiquitous in reconstructive orthopaedics and is a critical risk factor for the success of revision hip surgery.
We have recently developed a material with a tailored microlattice that is isoelastic, i.e. its strain energy matches locally that of the femoral bone tissue. The material is a graded cellular Ti-6Al-4V with optimized microarchitecture that possesses minute structural details. The functionally graded distribution of lattice properties is designed to simultaneously preserve bone stock and minimize implant micromotion, two antagonist objective functions that no implant in the market is able to reconcile. A methodology based on multiscale mechanics and multiobjective optimization is proposed to control the material microarchitecture and its properties. Asymptotic homogenization is used to capture the multiscale mechanics of the material, as well as the strain regime at both the macro and micro scales. An evolutionary optimization algorithm is used to handle the conflicting nature of bone resorption and implant interface failure. CT scan data of a 38 year-old male patient is used to reconstruct an accurate 3D model of the femur geometry with a realistic distribution of bone material. Cyclic pattern of forces during walking are applied to the hip and the lattice material of the implant is designed against fatigue failure. The building block of the cellular material has cell topology that maximizes bone ingrowth; its relative density is considered as the design variable in the multiobjective optimization of the graded material properties of the cellular material.
Ti-6Al-4V graded microlattice prototypes with minimally invasive shape are built with Electron Beam Melting. Compared with conventional titanium implants, our results show that a reduction of 70% of bone resorption and 50% of interface stress failure can be obtained with an isoelastic microlattice. This work can contribute to the development of a new generation of orthopaedic implants with cellular microarchitecture that can reduce the clinical consequences of bone resorption.

Freeze-drying is a method suitable for creating porous scaffolds of controllable permeability to be used in regenerative medicine applications. Nanometres-thin films of material form during the process, which constitute the walls of the pores. Their mechanical behaviour determines the one of the bulk structure and a correlation between the two is needed to control the range of properties required for tissue-specific applications. In the present work, collagen sponges were prepared by freeze-drying collagen suspensions of different concentrations, using different heat flow regimes. The properties of single pore membranes deposited on an array of circular wells were measured by colloidal probe atomic force microscopy, using a 5 mu;m diameter borosilicate glass spherical tip. Their structure and the orientation of the collagen fibrils within the film were also investigated using tapping mode atomic force microscopy with a silicon tip. The macro-scale mechanical and permeability properties of the bulk structure were measured to characterise its poroelastic behaviour. A relationship with the nano-scale properties of the thin membranes, as well as with simple process variables, was explicated in terms of cellular materials mechanics.

Lightweight periodic cellular metals have been widely used as the cores of sandwich panel structures for load supporting applications and numerous multifunctional applications such as heat exchange, dynamic load protection, and acoustic damping. Examples of core designs including lattice structures with tetrahedral, pyramidal, 3D-Kagome, prismatic corrugations, and metal wove textile topologies. The mechanical responses of the periodic cellular lattice structures are determined by the lattice topologies, core relative density and parent alloy mechanical properties. In this talk, we will present the designs and fabrication methods of two novel lattice structures which have not been reported to date, including (1) carburized stainless steel hollow tube collinear lattice structures and (2) Ti-6Al-4V alloy snap-fitting octet lattice structures. For the stainless steel collinear lattice structures, tubes have been used to serve as the trusses in order to increase the resistance to elastic buckling; carburization was performed to dramatically improve the strength of the parent material without the sacrifice of lattice density. For the Ti-6Al-4V octet lattices, a unique snap-fitting assembling technique has been introduced which allows for quick, easy and accurate large scale assembling. Vacuum brazing has been performed to bond the lattices together after initial truss assembling. Relative density of the lattices can be controlled by varying the geometry of the trusses; with appropriate geometry design, failure mechanism of such lattices is controlled by inelastic buckling of the trusses. Compared with other core topologies, the reported lattices are superior to competing metal core designs such as woven textiles and corrugations in specific compressive and shear strengths. The reported lattice structures can serve as promising candidate as lightweight sandwich cores for elevated temperature and multifunctional applications where both high strength and high energy absorption are required.

Microscale and mesoscale cellular materials, with their inherent capability to be architected on multiple length scales, have applications in multifunctional materials and systems. While most cellular materials show promise in lightweighting applications, open cellular materials also have additional multifunctional applicability in enhanced convective heat transfer. In particular, controlling their feature sizes on the micro- and mesoscales leads to high surface-to-volume ratio (compactness) and high convective heat transfer coefficients. Rational design of open cellular materials leads to lightweight, compact, and efficient heat sinks, cold plates, heat exchangers, and heat pipes.
Optimal design of multifunctional materials and systems requires physical laws for the system, constitutive models for the cellular material, and multiobjective optimization to handle the competing functionalities. We discuss the development of constitutive relationships for heat transfer and fluid flow through micro-lattices with solid and hollow lattice members via combined empirical and computational approaches. We then apply these constitutive equations in a multiobjective optimization framework to the design of multifunctional cold plates, planar heat pipes, and heat exchangers.

Recent advances in micromanufacturing techniques allow the fabrication of material microstructures with essentially arbitrary designs, including those with multiple materials and void space in nearly any shape. With an essentially open design space, the onus is on the engineer to design materials which are optimal for their purpose. We motivate our material design method by discussing our design problem, which requires consideration of the stiffness, conductivity, thermal expansion, and density of the architected material. We then describe our topology optimization-based method for designing isotropic materials with novel combinations of stiffness, thermal expansion, and thermal conductivity. We design a periodic unit cell and use homogenization theory to determine the bulk material properties, which enter into the objective and constraint functions of the optimization problem. We constrain the design space to satisfy material isotropy directly (2D), or to satisfy cubic symmetry (3D), from which point an isotropy constraint function is easily applied. This method is quite general and can extended to consider additional properties of interest. We have written a parallel implementation of this method to allow optimization with a large number of parameters in relatively short time.

Wheels are ubiquitous in transportation technology and serve multi-functional roles, as a function of vehicle application. Through vertical deformation, a compliant wheel expands ground contact area providing an increase in traction, improvement in ground pressure distribution and a decrease in wheel sinkage in soft soil. Compliance also serves to improve vibration and shock absorption on irregular terrain. Wheel deformation, however, can also lead to reduced rolling efficiency and handling. Pneumatic tires have evolved over the past 100 years offering a trade-off with the aforementioned performance metrics. Increasingly, however, there is a desire for developing airless tires for applications where tire puncture is unacceptable. This has motivated efforts to develop novel wheel concepts with non-pneumatic, non-rubber designs.
Lattice materials offer promising multi-functional properties pertinent to compliant wheel design. By controlling the microarchitecture of the lattice, the mobility performance of the wheel can be optimized for a specific application. In this work, a multi-objective optimization (MOO) problem is formulated to find optimal lattice microstructures for a wheel of a lunar rover. Three objective functions are considered in the MOO to evaluate the wheel&’s ability to develop traction, conduct a turning maneuver and reduce rolling resistance while ensuring the wheel does not deform plastically. The objective functions and constraints are evaluated in a time domain finite element analysis, where a wheel composed of a homogeneous material is driven over a terrain. The homogeneous properties of the wheel are determined by a multi-scale homogenization technique coupling the lattice microstructure and the macroscopic properties of the lattice material. This technique allows the resulting microscopic loading on the lattice geometry to be computed, while reducing the computational complexity of the FEA by simplifying the wheel as a homogeneous material. This results in a significant reduction of the computational effort required to solve the MOO, where a FEA is used to evaluate the objective functions at each iteration. Individual MOO problems are solved for three dimensional lattice materials. The results of this work compare various lattice topologies for compliant wheel applications.

We exploit the ability of shape memory polymers to fix a thermo-mechanically programmed deformation and the strong dependence on the cell geometry of the effective properties of periodic cellular materials to demonstrate a new class of programmable materials. The effective properties of these materials can be varied after they have been manufactured without requiring any reprocessing. The reachable property space depends on the base material, the unit cell geometry and the programmed geometric imperfection at the cell level. We explore two different material systems within this class: one is based on a regular hexagonal honeycomb and the other is based on the Kagome honeycomb. Experiments show that significant changes in the effective properties (e.g. 55% increase in initial in-plane modulus, a 69% increase in the propagation stress for in-plane crushing and a 30% reduction in the out-of-plane flexural modulus for one material design) are attainable even with small magnitudes (e.g. global strain of 5%) of programmed imperfections. We show that some material systems are capable of bi-directional modulation of some properties while others are restricted to uni-directional modulation when we limit the material design to include only homogeneous imperfections.

Periodic lattice structures can have much higher specific strengths than stochastic foams, giving the lattice structures potential to outperform foams in many applications, including energy absorption. The greatest potential benefit over stochastic foams lies at low relative densities (< ~5%). To achieve such low relative densities, the lattice structure must be composed of slender struts, which during compression are prone to buckling, thereby reducing the amount of energy absorbed. Previous attempts to stabilize the struts against buckling include filling the void space within the lattice with a stochastic foam. While effective in delaying buckling, placing all of the mass within the composite into the lattice structure alone has been proven more efficient. We examine a new concept of bracing the lattice structure to delay buckling by introducing discrete struts in key locations. Results show that by bracing with smaller length-scale struts (introducing hierarchy), structures can be created that exceed the specific performance of the lattice alone. An evolutionary optimization algorithm, paired with a finite element code, is used to explore the vast design space for the optimal structure. The metrics of interest (weight, strength, and energy absorbed) are evaluated for each individual design, and are combined in a fitness function to allow for comparing structures with different topologies. Promising designs are selected to undergo crossover and mutation algorithms and generate offspring. Repeating the process with the offspring allows the beneficial traits of each individual to survive with slight modification to converge to an optimal solution.

Recent advances in manufacturing allow fabrication of single and multi-phase cellular materials with unprecedented topological complexity. Optimal design of these topologies could potentially result in unprecedented performance in a number of metrics. The powerful technique of topology optimization (whereby the optimal arrangement of a number of phases - including voids - within a design domain is sought to maximize a prescribed performance metric subject to prescribed constraints) is an ideal tool for the optimal design of periodic architected materials. Although stiffness optimization of two-phase lightweight structures and materials has been extensively investigated, the application of topology optimization to more complex objective functions in multi-phase material systems is still in its infancy. In this presentation, we will discuss the optimal design of metal/elastomer cellular materials for optimal vibration damping. The elastomer is modeled as a visco-elastic material with complex elastic moduli, and the damping capacity of the periodic domain is analyzed by means of the Bloch-Floquet&’s theorem, thus allowing investigation of the effect of wave directionality, architecture and intrinsic material dissipation on the effective performance of the multi-phase cellular solid. A classic figure of merit for vibration damping of plates is maximized.

Topology optimization is a systematic, computational approach to the design of structure, defined as the layout of materials (and pores) across a domain. Typically employed at the component-level scale, topology optimization is increasingly being used to design the architecture of high performance materials, where architecture is defined as structural features at the hundreds of microns scale. The resulting design problem is posed as an optimization problem with governing unit cell and upscaling mechanics embedded in the formulation, and solved with formal mathematical programming.
This paper will describe the latest advances in topology optimization, including incorporation of manufacturing processes (etching, deposition, weaving, etc) and objectives governed by nonlinear mechanics and multiple physics, and demonstrate their application to the design of cellular materials. Combinations of mechanical, thermal, and fluid flow properties are considered. Optimized material architectures are shown to (computationally) approach theoretical bounds when available, and can be used to generate estimations of bounds when such bounds are unknown.

Lightweight porous metallic materials are generally created through specialized processing techniques. Their unique structure gives these materials interesting properties which allow them to be used in diverse structural and insulation applications. In particular, highly porous Al structures (Al foams) have been used in aircraft components and sound insulation; however due to the difficulty in processing and random nature of the foams, they are not well understood and thus they have not yet been utilized to their full potential. The objective of this project was to determine whether a relationship exists between the relative density (porous density/bulk density) and the mechanical properties of Al foams. For this purpose, a combination of computer simulations and experiments was pursued to better understand possible relationships. Models of the foam were generated using a combination of an open source software, Voro++, and MATLAB. A Finite Element Method (FEM)-based software, COMSOL Multiphysics 4.3, was used to simulate the mechanical behavior of Al foam structures under compressive loads ranging from 1-100 MPa. From these simulated structures, the maximum von Mises stress, volumetric strain, and other properties were calculated. These simulation results were compared against data from compression experiments performed using the Instron Universal Testing Machine (IUTM) on ERG Duocel open cell Al foams with 4-6% relative density. CES EduPack software, a materials design program, was also used to estimate the mechanical properties of open cell foams for values not available experimentally, and for comparison purposes. This program allowed for accurate prediction of the mechanical properties for a given percent density foam, and also provided a baseline for the Al foam samples tested via the IUTM method. Predictive results from CES EduPack indicate that a 4-6% relative density foam will have a Young&’s Modulus of 0.076-0.186 GPa while its compressive strength will be 0.497-1.280 MPa. Vendor data indicates a Young&’s modulus of 0.14 GPa with a compressive strength of 2.17 MPa. Overall results indicated that a combination of experiments and FEM simulations can be used to calculate structure-property relationships and to predict yielding and failure, which may help in the pursuit of simulation-based design of metallic foams. In the future, more robust modeling and simulation techniques need to be explored, as well as investigating closed cell Al foams and different porous geometries (nm to mu;m). This study can help to improve the current methods of characterizing porous materials and enhance knowledge about their properties for alternative energy applications, while promoting their design through integrated approaches.