We present a systematic methodology, built within the Open Knowledgebase of Interatomic Models (OpenKIM) framework (https://openkim.org), for quantifying properties of grain boundaries (GBs) for arbitrary interatomic potentials (IPs), GB character, and lattice structure and species. The framework currently generates results for symmetric tilt GBs in cubic materials, but can be readily extended to other types of boundaries. In this paper, GB energy data are presented that were generated automatically for Al, Ni, Cu, Fe, and Mo with 225 IPs; the system is installed on openkim.org and will continue to generate results for all new IPs uploaded to OpenKIM. The results from the atomistic calculations are compared to the lattice matching model, which is a semi-analytic geometric model for approximating GB energy. It is determined that the energy predicted by all IPs (that are stable for the given boundary type) correlate closely with the energy from the model, up to a multiplicative factor. It thus is concluded that the qualitative form of the GB energy versus tilt angle is dominated more by geometry than the choice of IP, but that the IP can strongly affect the energy level. The spread in GB energy predictions across the ensemble of IPs in OpenKIM provides a measure of uncertainty for GB energy predictions by classical IPs.

Data-driven interatomic potentials (IPs) trained on large collections of first principles calculations are rapidly becoming essential tools in the fields of computational materials science and chemistry for performing atomic-scale simulations. Despite this, apart from a few notable exceptions, there is a distinct lack of well-organized, public datasets in common formats available for use with IP development. This deficiency precludes the research community from implementing widespread benchmarking, which is essential for gaining insight into model performance and transferability, and also limits the development of more general, or even universal, IPs. To address this issue, we introduce the ColabFit Exchange, the first database providing open access to a large collection of systematically organized datasets from multiple domains that is especially designed for IP development. The ColabFit Exchange is publicly available at https://colabfit.org, providing a web-based interface for exploring, downloading, and contributing datasets. Composed of data collected from the literature or provided by community researchers, the ColabFit Exchange currently (September 2023) consists of 139 datasets spanning nearly 70 000 unique chemistries, and is intended to continuously grow. In addition to outlining the software framework used for constructing and accessing the ColabFit Exchange, we also provide analyses of the data, quantifying the diversity of the database and proposing metrics for assessing the relative diversity of multiple datasets. Finally, we demonstrate an end-to-end IP development pipeline, utilizing datasets from the ColabFit Exchange, fitting tools from the KLIFF software package, and validation tests provided by the OpenKIM framework.

Solenoids, ubiquitous in electrical engineering applications, are devices formed from a coil of wire that use electric current to produce a magnetic field. In contrast to typical electrical engineering applications that pertain to their magnetic field, of interest here is their use as actuators by studying their mechanical deformation. An analytically tractable model of parallel, coaxial circular rings is used to find the solenoid's axial deformation when subjected to a combined electrical (current) and mechanical (axial force) loading. Both finite and infinite solenoids are considered and their equilibrium configurations as well as their stability are investigated as functions of their geometry and applied current intensity.

In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these tools with the Open Knowledgebase of Interatomic Models and study three models based on the Lennard-Jones, Morse, and Stillinger-Weber potentials. We confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes in some parameter combinations. Because the inverse problem in such models is ill-conditioned, parameters are unidentifiable. This presents challenges for traditional statistical methods, as we demonstrate and interpret within both Bayesian and frequentist frameworks. We use information geometry to illuminate the underlying cause of this phenomenon and show that IPs have global properties similar to those of sloppy models from fields, such as systems biology, power systems, and critical phenomena. IPs correspond to bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of uncertainty quantification analysis and further suggest simplified, less-sloppy models.

Of interest here is the stability and associated deformation localization of structures when inertial effects are considered. Concerned primarily with the study of necking failure patterns, the prevailing approach in the relevant literature uses the “ modal analysis ” method to find the wavelength of the structure’s fastest growing eigenmode, an approach that often uses a rate-dependent material response. However, the experimental studies of (Zhang and Ravi-Chandar in Int. J. Fracture 142: 183–217, 2006 ; Zhang and Ravi-Chandar in Int. J. Fracture 163: 41–65, 2010 ) on the high strain-rate expansion of thin rings and tubes, show no evidence of a dominant wavelength in their failure mode and no influence of strain-rate sensitivity on the necking strains. Moreover, modal analysis assumes that at all times the entire structure sees the applied eigenmode perturbation in spite of the physical limitation of a finite wave propagation speed. In addition, the closely related problem of stability in dynamically loaded structures, i.e., the time evolution of perturbations introduced at different times during loading, does not seem to have attracted attention. Based on the above-mentioned experimental and theoretical observations, (Ravi-Chandar and Triantafyllidis in Int. J. Solids Struct. 58: 301–308, 2015 ) proposed a “ localized perturbation ” approach to study the dynamic stability of an incompressible, nonlinearly elastic bar at different strain-rates by following the evolution of spatially localized small perturbations introduced at different times. The goal of the present work is to study the dynamic stability – linear and nonlinear – of rate-independent biaxially strained thin plates by following the evolution of spatially localized perturbations introduced at different times, to understand the initiation of the corresponding failure mechanisms. Our 2D linearized analysis of a thin plate under plane stress state, shows that these plates are stable until τ _L , the dimensionless limit time corresponding to the loss of the uniformly strained plate’s stability. This result is supported by fully nonlinear calculations. Our nonlinear numerical calculations also show an imperfection amplitude-dependent and biaxiality-dependent delay in the appearance of localization patterns in dynamically loaded plates for dimensionless times well beyond τ _m , corresponding to the onset of loss of ellipticity in the constitutive law. Moreover, the failure patterns of these plates are studied numerically by following the time evolution of randomly distributed imperfections of different amplitudes.

We consider creases and folds in compressed hyperelastic solids from the point of view of bifurcation theory. They refer to highly localized surface deformations that occur at compressive loads significantly below the value of the well-known Biot instability. Much work from the literature attempts to make the case that this phenomenon corresponds to a ``local bifurcation'' distinct from the Biot instability. A local bifurcation is a path of equilibrium solutions emanating from a (bifurcation) point on the trivial solution branch that exists in all sufficiently small neighborhoods of that bifurcation point. The inference is usually made by first introducing a small surface imperfection; a solution curve is then obtained that is seemingly close to a perfect bifurcation diagram. However, imperfection theory is valid only in some sufficiently small neighborhood of a bifurcation point. Thus, in the absence of an equilibrium path connecting these solutions to the trivial one, there is no justification for concluding that creasing and folding are local bifurcations of the perfect system. In this work, we directly address the nucleation of these solutions in the perfect, imperfection-free case. We demonstrate that surface instabilities in functionally graded and bilayer elastic halfspaces, corresponding to local bifurcations from the homogeneous state, are necessarily smooth and oscillatory; creases/folds eventually do develop along the global bifurcating solution branches, albeit "far'' from the trivial solution, as evidenced by the corresponding bifurcation diagrams. In addition, we find that their stable realization occurs at load levels well below that of the initial surface instability. Moreover, we obtain such results for the perfect homogeneous halfspace, by switching the continuation parameter from macroscopic lateral strain to the film-to-substrate shear modulus ratio. When this ratio reaches unity, we obtain the desired localized deformation solution, avoiding the need for analysis near the highly degenerate homogeneous state at the Biot instability.

Interatomic potentials (IPs) are reduced-order models for calculating the potential energy of a system of atoms given their positions in space and species. IPs treat atoms as classical particles without explicitly modeling electrons and thus are computationally far less expensive than first-principles methods, enabling molecular simulations of significantly larger systems over longer times. Developing an IP is a complex iterative process involving multiple steps: assembling a training set, designing a functional form, optimizing the function parameters, testing model quality, and deployment to molecular simulation packages. This paper introduces the KIM-based learning-integrated fitting framework (KLIFF), a package that facilitates the entire IP development process. KLIFF supports both physics-based and machine learning IPs. It adopts a modular approach whereby various components in the fitting process, such as atomic environment descriptors, functional forms, loss functions, optimizers, quality analyzers, and so on, work seamlessly with each other. This provides a flexible framework for the rapid design of new IP forms. Trained IPs are compatible with the Knowledgebase of Interatomic Models (KIM) application programming interface (API) and can be readily used in major materials simulation packages compatible with KIM, including ASE, DL POLY, GULP, LAMMPS, and QC. KLIFF is written in Python with computationally intensive components implemented in C++. It is parallelized over data and supports both shared-memory multicore desktop machines and high-performance distributed memory computing clusters. We demonstrate the use of KLIFF by fitting a physics-based Stillinger–Weber potential and a machine learning neural network potential for silicon. The KLIFF package, together with its documentation, is publicly available at: https://github.com/openkim/kliff.

Atomistic simulations are an important tool in materials modeling. Interatomic potentials (IPs) are at the heart of such molecular models, and the accuracy of a model's predictions depends strongly on the choice of IP. Uncertainty quantification (UQ) is an emerging tool for assessing the reliability of atomistic simulations. The Open Knowledgebase of Interatomic Models (OpenKIM) is a cyberinfrastructure project whose goal is to collect and standardize the study of IPs to enable transparent, reproducible research. Part of the OpenKIM framework is the Python package, KIM-based Learning-Integrated Fitting Framework (KLIFF), that provides tools for fitting parameters in an IP to data. This paper introduces a UQ toolbox extension to KLIFF. We focus on two sources of uncertainty: variations in parameters and inadequacy of the functional form of the IP. Our implementation uses parallel-tempered Markov chain Monte Carlo (PTMCMC), adjusting the sampling temperature to estimate the uncertainty due to the functional form of the IP. We demonstrate on a Stillinger–Weber potential that makes predictions for the atomic energies and forces for silicon in a diamond configuration. Finally, we highlight some potential subtleties in applying and using these tools with recommendations for practitioners and IP developers.

Morphological instabilities in soft solids with free surfaces lead to an array of deformation modes including wrinkling, creasing, folding and ridge localization. While homogeneous systems tend to form creases, stiff films over soft substrates usually exhibit surface waves. Here, we look to analytically investigate this transition through the effects of film stiffness and finite thickness on the post-bifurcation stability of these surface waves. By considering both the film and substrate as compressible Neo-Hookean solids, we apply bifurcation theory and Lyaponov–Schmidt–Koiter asymptotics to produce a phase diagram of the surface wave stability over the parameter space. While earlier works have studied the effect of film-to-substrate stiffness ratios for thin films on deep substrates in the incompressible setting, we consider the additional effects of both finite film thickness and Poisson ratio. To investigate the further evolution of these surface waves, we turn to computational methods through finite-element simulations with bifurcation branch-following techniques. We see that as the unstable surface waves evolve, they eventually lead to the beginnings of crease formation. Thus, when the surface waves are unstable, we would expect snap-back or snap-through behaviour leading to creases.

The Open Knowledgebase of Interatomic Models (OpenKIM) is an NSF Science Gateway that archives fully functional computer implementations of interatomic models (potentials and force fields) and simulation codes that use them to compute material properties. Interatomic models are coupled with compatible simulation codes and executed in a fully automated manner by the OpenKIM processing pipeline, a cloud-based computation platform. The pipeline as previously introduced in the literature was insufficient to support the large volume and scale of computations that have become necessary within the materials science community. Accordingly, we present extensions made to the pipeline that allow it to utilize High-Performance Computing (HPC) resources in an efficient and performant fashion.

uncertainty quantification of classical empirical interatomic potentials Yonatan Kurniawan, Cody L. Petrie, Kinamo J. Williams, Mark K. Transtrum, a) Ellad B. Tadmor, Ryan S. Elliott, Daniel S. Karls, and Mingjian Wen Department of Physics and Astronomy, Brigham Young University, Provo, UT 84604, United States Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, United States Energy Technologies Area, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, United States

Shape Memory Alloys (SMAs) are a class of materials with unusual properties that have been attributed to the material undergoing a martensitic phase transformation (MPT). Often in β-phase SMAs the austenite is a B2 cubic configuration that transforms into a modulated martensite (MM) phase. First-principles computational results have shown that the minimum energy phase for these materials is not a MM, but a short-period structure called the ground state martensite. To date, a general approach for predicting the properties of the MM structure that will be observed for a particular material model has not been available. In this work, we (I) demonstrate the existence of MMs through explicit atomistic simulations using the branch-following and bifurcation (BFB) method. The free-energy material model used in the BFB study was developed by Guthikonda and Elliott (2011) and was shown to capture the general behavior of typical β-phase SMAs. Through the BFB study, MMs are found to be natural features of the free energy landscape (expressed as a function of the lattice parameters and individual atomic positions within a perfect infinite crystal). This work also yields insight into the free energies of MMs relative to the ground state martensite and examines the effect of an austenite kinematic compatibility constraint which agrees with the justification of the experimental observation of metastable MMs as low-energy phases stabilized by the kinematic compatibility requirement during a MPT. (II) We present a framework for the interpretation of MMs as a mixture of two short-period base martensite phases. From only a small set of input data associated with the two base martensites the modulated martensite mixture model (M4) is capable of accurately predicting the energy, lattice constants, and structural details of an arbitrary MM phase. Finally, (III) the predictive capability of the M4 is demonstrated through the discovery and verification of a previously unidentified and highly compatible MM structure for the atomistic model of part (I).

The Open Knowledgebase of Interatomic Models (OpenKIM) is a framework intended to facilitate access to standardized implementations of interatomic models for molecular simulations along with computational protocols to evaluate them. These protocols include tests to compute material properties predicted by models and verification checks to assess their coding integrity. While housing this content in a unified, publicly available environment constitutes a major step forward for the molecular modeling community, it further presents the opportunity to understand the range of validity of interatomic models and their suitability for specific target applications. To this end, OpenKIM includes a computational pipeline that runs tests and verification checks using all available interatomic models contained within the OpenKIM Repository at https://openkim.org. The OpenKIM Processing Pipeline is built on a set of Docker images hosted on distributed, heterogeneous hardware and utilizes open-source software to automatically run test-model and verification check-model pairs and resolve dependencies between them. The design philosophy and implementation choices made in the development of the pipeline are discussed as well as an example of its application to interatomic model selection.

The mechanics of cellular honeycombs-part of the rapidly growing field of architected materials-in addition to its importance for engineering applications has a great theoretical interest due to the complex bifurcation mechanisms leading to failure in these nonlinear structures of high initial symmetry. Of particular interest to this work are the deformation patterns and their stability of finitely strained circular cell honeycomb. Given the high degree of symmetry of these structures, the introduction of numerical imperfections is inadequate for the study of their behavior past the onset of first bifurcation. Thus, we further develop and explain a group-theoretic approach to investigate their deformation patterns, a consistent and general methodology that systematically finds bifurcated equilibrium orbits and their stability. We consider two different geometric arrangements, hexagonal and square, biaxial compression along loading paths, either aligned or at an angle with respect to the axes of orthotropy, and different constitutive laws for the cell walls which can undergo arbitrarily large rotations, as required by the finite macroscopic strains applied. We find that the first bifurcation in biaxially loaded hexagonal honeycombs of infinite extent always corresponds to a local mode, which is then followed to find the deformation pattern and its stability. Depending on load path orientation, these first bifurcations can be simple, double or even triple. All bifurcated orbits found are unstable and have a maximum load close to their point of emergence. In contrast, the corresponding instability in square honeycombs always corresponds to a global mode and hence the deformation pattern will depend on specimen size and boundary conditions. (C) 2020 Elsevier Ltd. All rights reserved.

Two-dimensional molybdenum disulfide (MoS2) is a promising material for the next generation of switchable transistors and photodetectors. In order to perform large-scale molecular simulations of the mechanical and thermal behavior of MoS2-based devices, an accurate interatomic potential is required. To this end, we have developed a Stillinger-Weber potential for monolayer MoS2. The potential parameters are optimized to reproduce the geometry (bond lengths and bond angles) of MoS2 in its equilibrium state and to match as closely as possible the forces acting on the atoms along a dynamical trajectory obtained from ab initio molecular dynamics. Verification calculations indicate that the new potential accurately predicts important material properties including the strain dependence of the cohesive energy, the elastic constants, and the linear thermal expansion coefficient. The uncertainty in the potential parameters is determined using a Fisher information theory analysis. It is found that the parameters are fully identified, and none are redundant. In addition, the Fisher information matrix provides uncertainty bounds for predictions of the potential for new properties. As an example, bounds on the average vibrational thickness of a MoS2 monolayer at finite temperature are computed and found to be consistent with the results from a molecular dynamics simulation. The new potential is available through the OpenKIM interatomic potential repository at https://openkim.org/cite/MO_201919462778_000.

This paper explores the importance of nonlinear material properties in the design of hierarchical honeycomb materials. The recent literature on the design and optimization of linear material properties for hierarchical honeycombs is reviewed. Then a full nonlinear post-bifurcation numerical analysis is performed for five representative hierarchical honeycomb structures. Particular attention is paid to the following four nonlinear material properties: the critical load λc at which the structure first experiences an instability; the plastic critical load λp at which the onset of plasticity would occur (if no elastic instability occurred); the stable post-bifurcated structure of the honeycomb; and the purely elastic resilience of the nonlinear material. It is found that although the honeycomb’s linear Young’s modulus is optimally maximized at a hierarchy ratio of γ1 ≈ 30%, the critical load is reduced by a factor of two (relative to the standard honeycomb) at this ratio. Further, the critical load displays a monotone decreasing trend with increasing hierarchy ratio. A similar trend is found for the plastic critical load. A non-monotone trend for the resilience is discovered and explained by a qualitative change in the stable post-bifurcated structure for the hierarchical honeycombs which occurs as the hierarchy ratio is increased. The observed loss of strength (decreased critical load) is significant and may negate any advantages of the increased Young’s modulus. This result demonstrates the importance of considering nonlinear properties and their implications in the design and optimization of hierarchical materials.

Fitted interatomic potentials are widely used in atomistic simulations thanks to their ability to compute the energy and forces on atoms quickly. However, the simulation results crucially depend on the quality of the potential being used. Force matching is a method aimed at constructing reliable and transferable interatomic potentials by matching the forces computed by the potential as closely as possible, with those obtained from first principles calculations. The potfit. program is an implementation of the force-matching method that optimizes the potential parameters using a global minimization algorithm followed by a local minimization polish. We extended potfit. in two ways. First, we adapted the code to be compliant with the KIM Application Programming Interface (API) standard (part of the Knowledgebase of Interatomic Models project). This makes it possible to use potfit. to fit many KIM potential models, not just those prebuilt into the potfit. code. Second, we incorporated the geodesic Levenberg-Marquardt (LM) minimization algorithm into potfit. as a new local minimization algorithm. The extended potfit. was tested by generating a training set using the KIM environment-dependent interatomic potential (EDIP) model for silicon and using potfit. to recover the potential parameters from different initial guesses. The results show that EDIP is a 'sloppy model' in the sense that its predictions are insensitive to some of its parameters, which makes fitting more difficult. We find that the geodesic LM algorithm is particularly efficient for this case. The extended potfit. code is the first step in developing a KIM-based fitting framework for interatomic potentials for bulk and two-dimensional materials. The code is available for download via https://www.potfit.net.

University of Minnesota Ph.D. dissertation. April 2016. Major: Aerospace Engineering and Mechanics. Advisors: Ryan Elliott, Ellad Tadmor. 1 computer file (PDF); xii, 273 pages.