Symposium CM4 : Verification, Validation and Uncertainty Quantification in Multiscale Materials Simulation

Combining theory, models and simulation, computational materials science has become the third leg of materials discovery and development, along with materials synthesis and characterization. While the analysis of errors is quite well developed for experiments, such analysis for simulations, particularly for simulations linked across length and time scales, is much less advanced. In this talk we will discuss the two extremes of the types of multiscale simulations, sequential multiscale and concurrent multiscale, and the role that uncertainty quantification (UQ) can play in each. We will base the discussion on specific examples from the rather sparse literature on UQ in materials simulations. We will end by identifying needs for conceptual advances, needs for the development of best practices, and needs for specific implementations. This discussion will be based in part on a recent review article by the authors. [1]

[1] “Uncertainty quantification in multiscale simulation of materials: A prospective,” A. Chernatynskiy, S. R. Phillpot and R. LeSar, Annual Review of Materials Research 43, 157-182 (2013).

During the development of interatomic empirical potentials, functions are typically fit to known material properties of specific atomic structures. For each scenario in the training set, an objective function is defined as the sum squared error between predicted and target values. Since parameters of empirical potentials typically affect multiple quantities of interest, the simultaneous minimization of all objective functions is typically not possible. Multiple objective functions are coupled through a weighted sum of squares in which higher weights force greater fidelity toward a specific material property, at the expense of a possible loss of fidelity in other predicted quantities. Although these weights are not formally part of an empirical potential, they directly affect the parameterization. Since the training set is typically small and spans different material phases, parameterization can be highly sensitive to the choice of weights. We treat weights as hyperparameters and present techniques to choose weights that deliver models with good performance when there are small departures in parameterized values. An example using the Embedded Atom Model (EAM) for Ni is used to demonstrate techniques developed.

Accuracy of interatomic potentials are essential in identifying and predicting atomic scale mechanisms through the use of molecular dynamic simulations. These atomic mechanisms, especially those involving chemical reactions, require careful fitting of complex potentials which can contain hundreds of fitting parameters. One such potential is the ReaxFF, which aims to be an one-fits-all potential across different structural and chemical systems. Therefore, fitting these robust potentials often leads to compromises on the potentials ability to accurately simulate a specific system. This seems to be true for boron carbide, where we have found significant deviations between the potential and ab initio calculated mechanical properties. Nonetheless, ReaxFF is an excellent starting point for complex systems such as boron carbides. To understand the potentials’ sensibility to variations of these fitting parameters, we have performed a systematic study of two different parameterizations of the ReaxFF. First, we employed the one-factor-at-a-time method by varying specific parameters between the two potentials. The parameters to modify were chosen based on a relative difference criterion between the two parameterizations, i.e. largest variability between the fittings. This study allows us to directly compare and quantify ReaxFF’s sensibility to a unique fitting parameter. This provides a limited understanding of the potential’s sensitivity to variations of the many fitting parameters defined the ReaxFF. Therefore, we also applied the design of experiments methodology to quantify the overall behavior of ReaxFF by simultaneously varying multiple factors. The computational experiment is clearly an advantageous formulation to identifying and quantifying the relationship between the fitting parameters and the ReaxFF’s ability to accurately describe the boron carbide structure.

Failure mechanisms of poly(p-phenylene terephthalamide (PPTA) under extreme tensile deformation has been studied using reactive potentials with molecular dynamics simulations. Amorphous PPTA systems with different molecular weights generated using an in-house developed amorphous builder. Tensile modulus of amorphous PPTA has been calculated as up to 6.7 GPa. Nitrogen and carbon vacancy defects were introduced to both crystalline and amorphous systems. The tensile modulus of defects-free crystalline PPTA calculated as 350 GPa. Introduction of 5\% nitrogen vacancy defects reduced the tensile modulus to 197 GPa. To estimate fiber modulus, PPTA fiber considered to be composed of amorphous and crystalline phases. Rule of mixtures formula modified to incorporate influence of defects on tensile modulus. Histograms of various quantities such as bond lengths, bond angles and phenyl ring diameters were calculated at different strain levels. Tensile load was mostly accommodated through stretching of bonds between amide group and phenyl groups. Under extreme tensile deformation PPTA chains failed at these C-N bonds.
MD simulations of PPTA fibers were carried out in three forms. In first form PPTA chains were in crystal order. In second form chains were unordered. PPTA fibers with chains were in crystal order have higher tensile strength due to inter chain bondings. In last form core-shell structures of PPTA fibers in which unordered chains reside in core region and crystal structure resides in shell region were modeled. All three forms of PPTA fibers were compared in order to understand and validate structure property relations.

We report the development of a new exchange-correlation functional from the point of view of machine learning [1]. Using atomisation energies of solids and small molecules, we train a linear model for the exchange enhancement factor using a Bayesian approach which allows for the quantification of uncertainties in the predictions. A relevance vector machine is used to automatically select the most relevant terms of the model. We then test this model on atomisation energies and also on bulk properties. The average model provides a mean absolute error of 0.116 eV for the test points of the G2/97 set but a larger 0.314 eV for the test solids. In terms of bulk properties, the prediction for transition metals and monovalent semiconductors has a very low test error. However, as expected, predictions for types of materials not represented in the training set such as ionic solids show much larger errors. Connections will be made with a recently proposed Machine Learning approach capable of learning on-the-fly from Quantum Mechanical forces [2].

[1] M. Aldegunde, J.R. Kermode and N. Zabaras, Submitted (2015).
[2] Z. Li, J. R. Kermode, and A. De Vita, Phys. Rev. Lett. 114, 096405 (2015).

Modeling the aging of metal tritides---tritium decay, helium migration, bubble nucleation and growth, and rupture---requires detailed knowledge of the mechanical properties of the tritide material. Reliable data of needed accuracy is often not available from direct measurements, due to challenges in sample generation and interpretation of experiments. Calculations using density functional theory are very good at modeling mechanical properties of metals with high precision, and can generate very accurate data---or can they? We describe the careful attention to the numerical aspects of the DFT modeling that inject uncertainties into the assessment of mechanical properties of the rare earth dihydrides at each stage of the analysis. The aggregated errors in the DFT simulations and in the upscaling into polycrystalline data incur errors as large as in the experiments. It is the interplay with experiments that allow meaningful validation and reliable estimation of parameters that are needed for mesoscale models of aging in tritides. In addition, this analysis provides interesting, and credible insights into the transitions between the cubic and tetragonal hydride phases that characterized the early transition metals and lanthanides.
Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Recent high-throughput ab-initio studies of transition metal binaries have suggested a great number of undiscovered stable phases present in well-studied systems. Co-Pt alloys, especially, have a long experimental history demonstrating three stable mixed phases: L1_0 CoPt and L1_2 Co_3Pt and CoPt_3, but density functional theory suggests a set of yet-unobserved long-period \beta_2-like superstructures at Pt-rich compositions. By fitting the ab-initio results to a cluster expansion Hamiltonian appropriate for use in Monte Carlo simulations, we show that the resulting high-temperature phase diagram is wholly incompatible with experimental results[1]. The failure of density functional theory to treat Co-Pt and related materials motivates an experiments-driven approach to cluster expansion parameters, e.g., via fluctuation microscopy. The case study of Co-Pt demonstrates a broader need to use coarse-graining techniques and statistical mechanics to bridge the comparison gap between zero-Kelvin simulation results and high-temperature experimental observations. [1] E. Decolvenaere, M.J. Gordon, A. Van der Ven, Phys. Rev. B 92, 085119 (2015)

Transition metal (TM) oxides are important material class with diverse applications spanning devices, environment and energy applications. In many applications, detailed atomic structures of the TM oxides are important in determining their functional properties. Full quantum simulations such as density functional theory (DFT) method have provided many accurate atomic and electronic structure information, but these understanding is limited to a very small system size of 100-1000 atoms. For micro-scale structures simulations, e.g., multiple phases and interfaces in-between, full quantum simulation faces challenging computational problems. MEAM is a very accurate semi-empirical inter-atomic potential which can model both metallic and covalent bonding interactions in metals and semiconductors. While for the ionic bonding in TM compounds, the long range Coulomb interaction due to charge transfer among atoms should be considered. By combining the charge transfer (CT) and the corresponding short range non-ionic interaction with MEAM, we have developed a CT-MEAM method to describe TM oxides, specifically manganese oxides for energy storage and conversion materials modeling. Properties derived from this method match quite well with the corresponding DFT reference work and essential atomic structure behaviors (phase stability, defect structures, size effects, etc.) under scale of 0.1 - 10 microns and larger time scale have been modeled. The presented simulation method can help facilitate large-scale atomic calculations required for the optimal design of many TM oxides applications.

This work was supported by Samsung GRO project.

Atomistic descriptors including net atomic charges (NACs), atomic spin moments (ASMs), bond orders, atomic polarizabilities, and C₆ dispersion coefficients play a key role in multi-scale materials modeling. NACs are widely used to quantify electron transfer among atoms in materials and to construct electrostatic force-field models for classical molecular dynamics and Monte Carlo simulations. ASMs quantify the structure of magnetic materials at the atomic level (e.g., ferromagnetic, anti-ferromagnetic, ferrimagnetic). Bond orders are crucial to understanding chemical bonding in every kind of material. Atomic polarizabilities are a key descriptor for construcing polarizable force-fields. Dispersion coefficients are used to model the London dispersion interactions between chemical species.

We construct a new atomic population analysis method, called DDEC6, based on rigorous physical principles. We show the conventional viewpoint that the properties of atoms-in-materials are ill-defined is both unnecessary and scientifically incorrect. We show NACs, ASMs, bond orders, atomic polarizabilities, and C₆ dispersion coefficients can all be accurately computed at the same time from the physically motivated DDEC6 electron density partitioning. This revolutionary finding is supported by extensive comparisons to experimental data for a wide variety of material types: small molecules and ions; large biomolecules; ionic, covalent, and metallic solids; porous and nonporous solids; solid surfaces; nanostructures materials; and materials with collinear and non-collinear magnetism. Our computational tests are drawn from a diverse set of more than 50 different chemical elements from the lightest to the heaviest, including s-block, p-block, d-block, and f-block elements. For small molecules, our computed C₆ dispersion coefficients are within ~4% of the experimental values. For both molecules and dense solids, our computed static system polarizabilities are within ~10% of the experimentally derived values. For magnetic materials, our computed ASMs are in excellent agreement with polarized neutron diffraction experiments. Our method computes accurate bond orders across the widest range of material types: ionic and covalently bonded materials, metallic conductors (e.g., transition metal solids), organometallic complexes, hydrogen bonded materials, materials with delocalized and resonant bonding (e.g., B₂H₆, aromatic materials), materials with weak dispersion bonds (e.g., noble gas dimers), materials with collinear or non-collinear magnetism, and periodic and non-periodic materials. The DDEC6 NACs are correlated to experimental spectroscopic data for various materials. Using numerous examples with quantitative accuracy assessment, we show DDEC6 NACs are ideally suited both for quantifying electron transfer between atoms-in-materials and for constructing flexible force-fields for classical molecular dynamics and Monte Carlo simulations of advanced materials.

To validate multiscale simulation models, it is necessary to consider evidence collected at a length scale that is different from the one at which a model predicts. In addition, epistemic and aleatory uncertainties need to be distinguished for more robust decision making. In this study, a Bayesian approach with generalized interval probability is taken for model parameter validation. A generalized interval Bayes’ rule (GIBR) is used to combine the evidence and update belief in the validity of parameters. The method is first applied to validate the parameter set for a molecular dynamics simulation of defect formation due to radiation. It is then applied to combining the evidence from two models of crystal plasticity at different length scales.

The Nuclear Energy Advanced Modeling and Simulation (NEAMS) program is developing the mesoscale tool MARMOT. MARMOT predicts the coevolution of microstructure and physical properties in reactor fuel and cladding materials. MARMOT is a critical part of the NEAMS program’s development of materials models for fuel performance based on microstructure. However, to ensure accuracy of the tool, we are working to validate the fracture and heat transfer models against detailed microstructure data. In addition, we are quantifying the uncertainty in the models.

For several years, CEA (French Atomic Energy Commission) has been developing the fuel performance code ALCYONE that allows the modelling and simulation of a whole nuclear fuel rod in irradiation conditions. This code calculates quantities such as strain, stress, inner pressure in the fuel rod and temperature of the fuel that can be related to safety criteria. To evaluate the confidence in the calculated results and to complete the best-estimate analysis, uncertainty quantification methods are now applied to this system.
Thermal-mechanical behavior is modeled using macroscopic properties such as thermal conductivity, creep behavior. But most of the physical phenomena such as fission gas release and swelling are modeled at a mesoscopic scale (grain size scale). Uncertainty quantification and sensitivity analysis are performed for both types of models.
Most of the physical phenomena occurring in nuclear fuel during its irradiation in reactor are driven by temperature. In the simulation process, the response of the models describing these phenomena is mainly conditioned by the confidence in the calculated temperature of the fuel. In the case of in reactor irradiation of fuel, several quantities that affect directly the temperature are uncertain, such as the linear heat rate of the fuel rod, the thermal conductivity of the fuel and the radial distribution of power in the fuel pellet due to neutron physics. Experimental data of material properties such as thermal conductivity are uncertain and scattered, especially in the case of irradiated fuel. Uncertainty quantification and sensitivity analysis is performed to quantify the uncertainty on the calculated temperature and also to identify which input factor affects the more this uncertainty. In order to consider possible interactions effects between the different parameters, a global method such as variance decomposition based method is used (Sobol’ indices).
Validation of models also uses probabilistic methods. Physical or numerical parameters are introduced in the modelling process that cannot be precisely measured. The first step of the validation process consists in the calibration of those parameters to make the model a “best-estimate” model on an experimental calibration database. Some probabilistic methods can be used to quantify the uncertainty on these parameters due to the uncertainty of the experimental data available. This is illustrated on a fission gas behavior model developed in the ALCYONE code.

One of the limitations of atomistic simulations is that many of the computational tools used to extract information from the atomic trajectories provide metrics that are not directly compatible with experiments for validation. For example, the centrosymmetry parameter is a very useful tool to identify dislocations, grain boundaries and other defects within an atomistic ensemble; however, it does not provide a direct route to experimentally verify the atomistic result. The primary objective of this work is to develop a computational approach to produce both x-ray diffraction profiles and electron diffraction patterns on-the-fly during atomistic simulations. In this computational technique, diffraction intensity is computed using the structure factor equation derived from kinematic diffraction theory applied over a high-resolution mesh of sampled points within reciprocal space, eliminating the need for a priori assumption of the material structure. Through appropriate data filtering and visualization, both x-ray 2θ line profiles and selected area electron diffraction patterns can be computed. Corrections are implemented to properly capture relrods when diffraction is conducted over a small volume, with comparison to diffraction theory for verification of relrod intensity as a function of diffraction volume. This approach is applied to study (1) Ni <001> symmetric tilt grain boundaries, (2) Al <111> symmetric twist grain boundaries, and (3) both homogeneous and heterogeneous interfaces in alumina. For grain boundaries in Ni and Al, virtual selected area electron diffraction patterns show subsidiary peaks directly attributed to the network of edge or screw dislocations within the grain boundary plane. For heterogeneous interfaces in alumina, the virtual diffraction technique allows experimental validation of the proper orientation relationship between crystalline domains at the interfaces.

Virtual x-ray and electron diffraction characterization from molecular dynamics simulations enables a unique route for model validation through direct comparison to both experimental and first principles data. In this work, virtual diffraction patterns are used to assess the fidelity of boron ceramic structures modeled by two parameterizations of the ReaxFF interatomic potential. Both selected area diffraction patterns and x-ray diffraction line profiles are generated through analysis of three-dimensional diffraction intensity maps by evaluating the structure factor equation across a high resolution reciprocal space mesh. Heterogeneous parallelization of the diffraction algorithm enables studying multimillion simulations, which in turn enables the study of defected structures in boron ceramics. Virtual diffraction patterns computed from single crystalline and defected boron ceramic simulations are compared to experiments and first principles in order to assess the capabilities and limitations of each ReaxFF parametrization.

We study computationally coarsening rates of the Cahn-Hilliard equation with a smooth double-well potential, and with phase-dependent diffusion mobilities. The latter is a feature of many materials systems and makes accurate numerical simulations challenging. Our numerical simulations confirm earlier theoretical predictions on the coarsening dynamics based on asymptotic analysis. We demonstrate that the numerical solutions are consistent with the physical Gibbs–Thomson effect, even if the mobility is degenerate in one or both phases. For the two-sided degenerate mobility, we report computational results showing that the coarsening rate is on the order of t^{1/4}, independent of the volume fraction of each phase. For the one-sided degenerate mobility, that is non-degenerate in the positive phase but degenerate in the negative phase, we illustrate that the coarsening rate depends on the volume fraction of the positive phase. For large positive volume fractions, the coarsening rate is on the order of t^{1/3} and for small positive volume fractions, the coarsening rate becomes t^{1/4}.

We present a thermodynamically consistent phase-field model using two sets of spontaneous polarization order parameters and a conserved composition field to describe the free energy of perovskite-based ferroelectric solid solutions containing morphotropic phase boundaries. The model is based on a two-parameter thermodynamic description of the ferroelectric solid solution lead zirconate-titanate [1]. The model integrates the spontaneous polarization order parameters with composition through the Gibbs free energy of mixing. The evolution of composition field is governed by the Cahn-Hilliard equation and the evolution of the polarization order parameters is described by a set of time-dependent Ginzburg-Landau equations. Additionally, we solve Poisson’s equation and mechanical equilibrium equation to account for the ferroelectric/ferroelastic interactions. We have performed three-dimensional simulations with appropriate electromechanical boundary conditions to study the effect of composition and applied strain on polarization switching. Moreover, we studied the effect of epitaxial strain on domain pattern formation in epitaxially grown single phase with morphotropic composition and multi-layered heterostructures consisting of alternating layers of terminal phases. Epilayers of single phase morphotropic composition was grown both under strained and relaxed conditions. We compare the simulated domain patterns and polarization hysteresis loops with those obtained experimentally in pseudobinary BZT-BCT systems using Piezoresponse Force Microscopy. We also discuss the variation in piezoelectric coefficient d₃₃ as a function morphotropic compositions.

e-mail: ms13m14p100001@iith.ac.in

References:
[1] Andrew J. Bell , Eugene Furman, Ferroelectrics, 293: 19–31, 2003

The phase diagrams are important tools to predict the behavior of materials at different conditions. The accuracy of the diagrams is of great importance. Recently, it has been turned out that there are discrepancies between some parts of the current YSZ (yttria stabilized zirconia) phase diagram and new experimental results. In this project, we will use the CALPHAD approach to modify the YSZ thermodynamic database. All the thermochemical and phase equilibria data related to YSZ system will be evaluated and the most accurate and reliable ones based on the experiment procedure will be selected. The Gibbs energy of the phases involved in the areas in which we observed discrepancies, will be modified upon the selected experimental data. The updated YSZ phase diagram will be plotted based on the improved thermodynamic database.

When two materials interact, the processes between the phases determine the overall properties of the new material. Pivotal interface phenomena are diffusion and redistribution of particles. This is especially of interest in Lithium ion batteries where the interfacial kinetics determines the battery performance and impact cycling stability. Hence, a simulation tool which investigates these processes is of fundamental interest. A new phase field model was developed in the OpenPhase framework*. This model links the atomistic processes to the mesoscale behavior by a parameter called ‘’interface permeability’’.The model was validated with experimental data from diffusion couples. Calculations of the concentration profiles of the species at the electrode-electrolyte interface are reported. Active particle size, morphology and spatial arrangement were put in correlation with diffusion behavior for use in reverse engineering. Furthermore, relationships between the interface permeability and electrochemical bulk properties are shown.

* www.openphase.de

The future management of nuclear ultimate waste requires pellet fabrication of uranium-americium mixed oxide as Minor Actinide Bearing Blanket (MABB) for the transmutation of americium in a sodium fast reactor [1]. In this context, this study is concerned with the pelletization of porous and spherical oxide precursors (lanthanides and/or uranium).
The present work uses both experimental data and numerical simulations to optimize the pelletization step. The final aim is to obtain, after sintering, homogeneous, dense and undistorted ceramic pellets. Oxide microsphere precursors are produced by the Weak Acid Resin process [2], which consists in loading beads of ion exchange resin with lanthanides and/or uranyle cations and mineralizing the metal loaded resin leads into oxide microsphere (diameter approximately 500 µm). The mechanical properties of a single microsphere were characterized experimentally by recording a series of crushing tests using a micro press synchronized with an optical camera in order to measure the strength and visualize fracture modes. In situ compression tests were also carried out in a Scanning Electron Microscope (SEM) to follow the crushing behavior with a larger magnification.
These highly porous microspheres are composed of micronic porous aggregates, which are themselves made of individual grains. We use the Discrete Element Method [3] (DEM) to model these different length scales. Because the full simulation of a microsphere at the length scale of grains would involve prohibitive CPU time, we first simulate the behavior of two idealized spherical aggregates where grains are modelled as bonded spheres. Building on these simulations, a full microsphere was then modelled as a porous assembly of spherical aggregates bonded together by solid bonds. The stiffness and strength of these individual bonds are fitted to obtain a good match with the macroscopic crushing behavior of a microsphere (Figure 1).
The last step consists in simulating the uniaxial compaction of a large number of oxide precursors (microspheres), for which rearrangement and breakage play an important role. Simulation results allow a direct relationship between applied pressures and microstructure. In particular, in conjunction with experimental compaction data, simulations enable a better understanding of effect of the applied pressure on the microstructure. This knowledge will help in determining the minimum pressure leading to a dense and homogeneous green pellet [4].

References:
[1] Warin, D. J. Nucl. Sci. Technol. 2007, 44, 410.
[2] Picart, S.; Mokhtari, H.; Jobelin, I., Patent, WO 2010/034716, 2010.
[3] Martin, C. L.; Bouvard, D.; Shima, S. J. Mech. Phys. Solids 2003, 51, 667.
[4] Pizette, P.; Martin, C. L.; Delette, G.et al. J. Eur. Ceram. Soc. 2013, 33, 975.

Amorphous solids, which lack crystal structure, find wide application from consumer goods to photovoltaics, but issues quantifying disorder have stymied reliable mechanical constitutive laws for these materials. Quantitatively predicting strain localization, a limiting failure process in high-strength metallic glasses and other amorphous materials, requires adequately capturing fluctuations in material structure and their interactions via the material’s mechanical response. We directly cross-compare molecular dynamics simulations and continuum representations of these same materials in order to test and validate our constitutive theories. We will discuss the role of uncertainty quantification in the validation of these theories and in making connections between atomistic and continuum theories through coarse-graining strategies.

Understanding the complex and inherently multi-scale interface between a charged electrode surface and a fluid electrolyte would inform design of more efficient and less costly electrochemical energy storage and conversion devices. Joint density-functional theory (JDFT)¹ bridges the relevant length-scales by joining a fully ab initio description of the electrode with a highly efficient, yet atomically detailed molecular DFT description² of the liquid electrolyte structure. First, we describe a universal approximation to the functional which couples any quantum-mechanical solute system with a molecular DFT for any liquid. We verify that JDFT calculations with this coupling functional capture aqueous and non-aqeuous solvation free energies of small molecules with a mean absolute error of only 1-2 kcal/mol. We also describe the procedure for calibrating molecular density-functionals for ionic species to reproduce the key features of ion-water correlation functions when combined in a mixture with existing functionals for water.

Leveraging the above theoretical innovations and our framework to treat charged systems in periodic boundary conditions,³ we then predict the voltage-dependent structure and energetics of solvated ions at the interface between an aqueous electrolyte and graphitic and single-crystalline metallic electrodes. We verify our predictions through comparison to ab initio molecular dynamics simulations, X-ray and neutron scattering measurements of liquid structure, and electrochemical capacitance measurements. We also explore the sensitivity of our predictions, estimating the errors inherent in JDFT using a sloppy model analysis inspired by Bayesian statistics. Such sensitivity analysis emphasizes the predictive power of JDFT compared to the highly empirical solvation models and classical pair potentials traditionally employed in multi-scale modeling.

¹ S.A. Petrosyan et al, Phys. Rev. B 75, 205105 (2007)
² R. Sundararaman, K. Letchworth-Weaver, T. A. Arias, J. Chem. Phys. 140, 144504 (2014)
³ K. Letchworth-Weaver and T.A. Arias, Phys. Rev. B. 86, 075140 (2012)

Classical molecular dynamics is a very powerful tool for elucidating lattice thermal conduction processes — particularly in nanoscale systems. The most ubiquitously used and numerically robust approach for computing lattice thermal conductivity is the Green-Kubo method. This equilibrium method is founded on the fluctuation dissipation theorem, and involves integrating the autocorrelation function of the heat flux fluctuations. These correlation functions can be noisy, and comprised of multiple relaxation times, and there is little systematic consensus in the literature on how best to numerically integrate them. In this work we present a detailed analysis of the uncertainty that arises from the numerical integration of these oscillation functions. Our approach is based on recognizing that the integration of the heat-flux noise is a random walk, and from this we can determine simulation and averaging conditions to optimally manage the uncertainty for a given allotment of computing resources.

We apply a recently developed ab initio informed mutiscale modeling approach based on the concept of the elastic dipole tensor to predict evolution of defects under complex strain fields. Our kinetic Monte Carlo simulations compute the diffusion rates of point defects, modified in the presence of external strains. The objective of this investigation is to establish the sources and propagation of uncertainties in various input parameters to our model across different length scales. The sensitivity of the overall diffusion rate on uncertainty in the values of each component of the defect dipole tensor, and on uncorrelated and correlated uncertainties in the various components, are analyzed. Preliminary results show that diffusivity is more sensitive to specific components of the dipole tensor and suggest possible coupling between different components of dipole tensor. AG and SRP were supported by a contract from Los Alamos National Laboratory.

The goal of the multi-institutional, multi-disciplinary Exascale Co-design Center for Materials in Extreme Environments (ExMatEx) is to establish the relationships between algorithms, software stacks, and architectures needed to enable exascale-ready materials science application codes within the next decade. We anticipate that we will be able to exploit hierarchical, heterogeneous architectures to achieve more realistic large-scale simulations with adaptive physics refinement, and are using tractable application scale-bridging proxy application testbeds to assess new approaches and requirements. Our focus has been on scale-bridging strategies that accumulate (or recompute) a distributed response database from fine-scale calculations, in a top-down rather than bottom-up multiscale approach. Such many-task computation workflows are driving the requirements for task-based programming models, databases, and runtime systems. The algorithmic challenges include how one identifies “nearby” previous fine-scale evaluations that can be used for interpolation, how this interpolation from the microstructure-response database is done, and how one determines whether interpolation is sufficiently accurate, or if a new fine-scale model evaluation must be launched. This latter question requires reliable error estimates, which can be obtained (with some assumptions) by kriging algorithms, or can be obtained by using different subsets of fitting points from the database, e.g. from differently randomized search trees in approximate nearest neighbor search techniques.

In general, concurrent multiscale methods have problems with dynamic reflections of waves at the interface between the fine scale and the coarse scale descriptions of materials. This issue could have a notable effect on the outcome of dynamic simulations such as dynamic plasticity in materials subjected to high strain rate deformations. In this work, the complex dynamics of sub-, trans- and supersonic dislocations in anisotropic crystalline materials is quantified through a concurrent atomistic-continuum (CAC) method. The CAC method is the numerical implementation of a unified continuum formalism, with the atomistic information being built in the formulation. We make a first attempt to characterize the complexity of fast moving dislocations in anisotropic crystals from atomistic to microscale within one single framework. When the dislocations migrate from the atomic to the continuum region, the energy intensities as well as the wavelengths of phonons emitted from the moving dislocations, and the velocity-dependent stress fluctuations around the core of dislocations are measured in CAC. The correlations between the dislocation mobility, the energetics and wavelengths of the emitted phonon waves are established from an atomic to a microscopic level. Effects of the presence of the atomistic/continuum interfaces on the instantaneous dislocation velocities and phonon drag effects on the dislocation mobility are investigated. Analysis of simulation results based on a wavelet transform show that the faster a dislocation is moving, the longer the emitted phonon wavelength. The long wavelength phonons are found to be smoothly transmitted from the atomistic to the continuum region and the short wavelength phonons are reflected back into the atomic region. The velocity of the subsequent dislocations fluctuates with the onset of the interactions between dislocations and the reflected waves. The effects of such dislocation-wave interactions on the dynamic properties of materials are quantified. CAC modeling framework is demonstrated to be the first multiscale method that explicitly treats the strong coupling between the long-range elastic fields away from the dislocation core, the highly nonlinear time-dependent stress field within the core, and the evolutions of the atomic-scale dislocation core structures. Tests of consistency between CAC simulation results and the existing dislocation mobility laws in crystalline materials are performed from atomistic to the microscale. The results are also compared with that from fully atomistic simulations to address the efficiency and convergence of the numerical algorithms implemented in CAC. The capability of CAC to describe the complex dynamics of sub-, trans-, and supersonic dislocations and to predict the dynamic properties of crystalline materials is assessed.

The mechanical behavior of metallic materials is governed by properties of the underlying microstructure. Understanding and predicting the structure-property relation is central to experimental and computational materials science. Over the last decades a large number of different simulation methods on various time and length scales has evolved. At the same time, advanced experimental characterization methods with high resolutions are able to reveal a rich variety of details about microstructural features. This offers a number of interesting possibilities, e.g. to use experiments for validating computational results on a microstructural level, or to use microstructure data from a 'lower scale' method (e.g. atomistics) - directly or indirectly - as input or for validation purposes for simulation method on larger scales. Up to date, however, methodologies for comparing and validating data from different methods are still lagging behind.

In this presentation we introduce our D2C (=discrete to continuous) approach¹, which can be used as novel 'language' for computationally characterizing dislocation microstructures: using orientation distributions we can mathematically compress dislocation data by means of a continuum description and the maximum information entropy principle. This data format can be tuned w.r.t. the level of compression and allows to directly compare dislocation microstructures from very different methods, e.g. MD simulations, TEM microscopy or tomography, continuum or DDD simulations. We show how our approach might serve as the foundation for a unified approach towards dislocation data, where one of the strengths of the D2C framework is that ensemble averages of statistically equivalent simulations/experiments can easily be performed. This is ideal for validation and data mining of in particular discrete methods (simulations as well as specialized experiments), whose microstructural data are often not easily accessible.

[1] S. Sandfeld and G. Po, Microstructural comparison of the kinematics of discrete and continuum dislocations models, Modelling and Simulation in Materials Science and Engineering, Volume 23, Number 8, 2015

A new pair potential that includes the effects of plasticity and strain hardening was developed and implemented as a new pair potential in the LAMMPS granular package to perform general particle dynamics (Discrete Element type) simulations. The contact model includes the normal component of the analytical contact model for impacts between spheres in [M.R.W. Brake, INT J SOLIDS STRUCT, Volume 62] in which a collision is assumed to have a period of elastic loading, followed by a period of elastic/plastic loading, followed by a period of elastic restitution. For validation, load-displacement curves obtained from simulated and experimental indentation of several metals were compared. The simulations consisted of two-particle displacement-controlled collisions, simulated in LAMMPS with this new pair style. The experimental data was collected using displacement-controlled indentation at load levels between 25mN and 10N with sub-nm resolution. The selected metals were 6061 Aluminum, titanium, bronze, annealed and unannealed copper and three stainless steels. It was found that the contact model found stronger agreement with indentations at low load levels (