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At least 865 records · Page 48

Inducing a tunable skyrmion-antiskyrmion system through ion beam modification of FeGe films

Abstract Skyrmions and antiskyrmions are nanoscale swirling textures of magnetic moments formed by chiral interactions between atomic spins in magnetic noncentrosymmetric materials and multilayer films with broken inversion symmetry. These quasiparticles are of interest for use as information carriers in next-generation, low-energy spintronic applications. To develop skyrmion-based memory and logic, we must understand skyrmion-defect interactions with two main goals—determining how skyrmions navigate intrinsic material defects and determining how to engineer disorder for optimal device operation. Here, we introduce a tunable means of creating a skyrmion-antiskyrmion system by engineering the disorder landscape in FeGe using ion irradiation. Specifically, we irradiate epitaxial B20-phase FeGe films with 2.8 MeV Au 4+ ions at varying fluences, inducing amorphous regions within the crystalline matrix. Using low-temperature electrical transport and magnetization measurements, we observe a strong topological Hall effect with a double-peak feature that serves as a signature of skyrmions and antiskyrmions. These results are a step towards the development of information storage devices that use skyrmions and antiskyrmions as storage bits, and our system may serve as a testbed for theoretically predicted phenomena in skyrmion-antiskyrmion crystals.

74 ATOMIC AND MOLECULAR PHYSICS↗

Quantifying dispersity in size and shape of nanoparticles from small-angle scattering data using machine learning based CREASE

Here, we use machine learning (ML) enhanced computational reverse engineering analysis of scattering experiments (CREASE) to interpret small-angle X-ray scattering (SAXS) data obtained from a system of nanoparticles without a priori knowledge of their exact shapes (e.g. spheres or ellipsoids), sizes (0.5–50 nm) and distributions. The SAXS measurements yielded three categories of scattering profiles exhibiting 'strong', 'weak' and 'no' features. Diminishing features (e.g. broadening or disappearing peaks) in scattering profiles have always been attributed to the presence of significant dispersity in the system. Such featureless SAXS data are not suitable for traditional analysis using analytical models. If one were to fit a relevant analytical model (e.g. the lmfit analytical model for polydisperse spheres) to these 'weak' and 'no' SAXS profiles from our nanoparticle systems, one would obtain non-unique interpretations of the data. Relying on electron microscopy to identify the distributions of nanoparticle shapes and sizes is also unfeasible, especially in high-throughput synthesis and characterization loops. In such situations, to identify the distributions of particle sizes and shapes that could be present in the sample, one must rely on methods like ML-CREASE to interpret the data quickly and output all relevant interpretations about the structure present in the system. The ML-CREASE optimization loop takes the experimental scattering profile as input and outputs multiple candidate solutions whose computed scattering profiles match the SAXS profile input. The ML-CREASE method outputs distributions of relevant structural features, such as the volume fraction of the nanoparticles in the system and the mean and standard deviation of the particle size and aspect ratio, assuming a type of distribution (e.g. normal, log-normal) for size and aspect ratio. We find that, for the SAXS profiles analyzed here, accounting for the shape dispersity along with size dispersity of the nanoparticles using ML-CREASE improved the match between the computed scattering profiles and input experimental profiles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NUMERICAL INVESTIGATION OF FUEL PROPERTY EFFECTS ON MIXED-MODE COMBUSTION IN A SPARK-IGNITION ENGINE

In the present study, mixed-mode combustion of an E30 fuel in a direct-injection spark-ignition engine is numerically investigated at a fuel-lean operating condition using multidimensional computational fluid dynamics (CFD). A fuel surrogate matching Research Octane Number (RON) and Motor Octane Number (MON) of E30 is first developed using neural network based non-linear regression model. To enable efficient 3D engine simulations, a 164-species skeletal reaction mechanism incorporating NO, chemistry is reducedfrom a detailed chemical kinetic model. A hybrid approach that incorporates the G-equation model for tracking turbulentflame front, and the multi-zone well-stirred reactor model for predicting auto-ignition in the end gas, is employed to account for turbulent combustion interactions in the engine cylinder. Predicted in-cylinder pressure and heat release rate traces agree well with experimental measurements. The proposed modelling approach also captures moderated cyclic variability. Two different types of combustion cycles, corresponding to purely deflagrative and mixed-mode combustion, are observed. In contrast to the purely deflagrative cycles, mixed-mode combustion cycles feature early flame propagation followed by end-gas auto-ignition, leading to two distinctive peaks in heat release rate traces. The positive correlation between mixed-mode combustion cycles and early flame propagation is well captured by simulations. With the validated numerical setup, effects of NOx chemistry on mixed-mode combustion predictions are investigated. NOx chemistry is found to promote auto-ignition through residual gas recirculation, while the deflagrative flame propagation phase remains largely unaffected. Local sensitivity analysis is then performed to understand effects of physical and chemical properties of the fuel, i.e., heat of evaporation (HoV) and laminar flame speed (S-L). An increased HoV tends to suppress end-gas auto-ignition due to increased vaporization cooling, while the impact of HoV on flame propagation is insignificant. In contrast, an increased SL is found to significantly promote both flame propagation and auto-ignition. The promoting effect of SL on auto-ignition is not a direct chemical effect; it is rather caused by an advancement of the combustion phasing, which increases compression heating of the end gas.

detailed chemical kinetics↗

Ultimate Suppression of Thermal Transport in Amorphous Silicon Nitride by Phononic Nanostructure.

Engineering the thermal conductivity of amorphous materials is highly essential for the thermal management of future electronic devices. Here, we demonstrate the impact of ultrafine nanostructuring on the thermal conductivity reduction of amorphous silicon nitride (a-Si3N4) thin films, in which the thermal transport is inherently impeded by the atomic disorders. Ultrafine nanostructuring with feature sizes below 20 nm allows us to fully suppress contribution of the propagating vibrational modes (propagons), leaving only the diffusive vibrational modes (diffusons) to contribute to thermal transport in a-Si3N4. A combination of the phonon-gas kinetics model and the Allen-Feldmann theory reproduced the measured results without any fitting parameters. The thermal conductivity reduction was explained as extremely strong diffusive boundary scattering of both propagons and diffusIons. These findings give rise to substantial tunability of thermal conductivity of amorphous materials, which enables us to provide better thermal solutions in microelectronic devices.

Tambo, Naoki↗

recon3d

SAND2025-00533O recon3d is a software tool that provides automated 3D reconstruction and meshing capabilities. It processes labeled 3D image data from various sources, starting from image stacks, and calculates 3D feature distributions like size, shape, and location. The software also has tools for downscaling rectilinear grid data and creating tetrahedral meshes directly from image data. recon3d can be used by novice users via the command line with a properly formatted configuration file. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Emery, John↗

Spatio-temporal Estimates of Disease Transmission Parameters for COVID-19 with a Fully-Coupled, County-Level Model of the United States

Sandia National Laboratories has developed a capability to estimate parameters of epidemiological models from case reporting data to support responses to the COVID-19 pandemic. A differentiating feature of this work is the ability to simultaneously estimate county-specific disease transmission parameters in a nation-wide model that considers mobility between counties. The approach is focused on estimating parameters in a stochastic SEIR model that considers mobility between model patches (i.e., counties) as well as additional infectious compartments. The inference engine developed by Sandia includes (1) reconstruction and (2) transmission parameter inference. Reconstruction involves estimating current population counts within each of the compartments in a modified SEIR model from reported case data. Reconstruction produces input for the inference formulations, and it provides initial conditions that can be used in other modeling and planning efforts. Inference involves the solution of a large-scale optimization problem to estimate the time profiles for the transmission parameters in each county. These provide quantification of changes in the transmission parameter over time (e.g., due to impact of intervention strategies). This capability has been implemented in a Python-based software package, epi_inference, that makes extensive use of Pyomo [5] and IPOPT [10] to formulate and solve the inference formulations.

42 ENGINEERING↗

Local Modification of Cast Aluminum Alloys via the Cast-and-Print Process

Casting of aluminum alloys is a cost-effective way to mass manufacture bulk aluminum parts for automotive applications. However, the casting process requires filling of a mold, which imposes some limitations on the geometries that can be successfully cast and limits parts to be a uniform material. Therefore, we proposed that a hybrid casting plus additive manufacturing approach, Cast-and-Print, which could be used to locally modify the properties and geometry of cast parts to create difficult-to-cast, functional features. Here, we report the results of the properties of deposited materials on cast substrate, the properties of the interface of the deposited and cast material, and the application of the Cast-and-Print method to deposit rivet tabs on high-pressure die cast plates. Ultimately, the approach appears viable, but there are engineering challenges present to reliable additive processing of aluminum wires that need to be overcome for successful implementation of the technology.

42 ENGINEERING↗

IDAES-PSE 2.2.0 Release

The Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform is a versatile computational environment offering extensive process systems engineering (PSE) capabilities for optimizing the design and operation of complex, interacting technologies and systems. IDAES enables users to efficiently search vast, complex design spaces to discover the lowest cost, most environmentally sustainable solutions while supporting the full process modeling lifecycle, from conceptual design to dynamic optimization and control. The extensible, open platform empowers users to create models of novel processes and rapidly develop custom analyses, workflows, and end-user applications. New features in the 2.2 release include: DiagnosticsToolbox DiagnosticsToolbox (idaes.core.util.model_diagnostics. DiagnosticsToolbox is a new self-guiding toolbox for assisting with diagnosing modeling issues. The toolbox contains a wide range of tools for identifying common modeling issues and conveying these to the user, and more features will be added in the coming months. To try the new toolbox, use the following steps: from idaes.core.util import DiagnosticsToolbox Build an instance of your model Ensure your models has zero degrees of freedom (as best you can) dt = DiagnosticsToolbox(model) dt.report_structural_issues() Follow the prompts Deprecations DegeneracyHunter is being deprecated in favor of the new DiagnosticsToolbox. The features and capabilities of DegeneracyHunter will be moved over to the DiagnositcsToolbox in the coming months. Removal of usage of Pyomo's expr.current due to deprecation upstream. Removed support for radial basis functions in ALAMOpy as these did not work in the current implementation. Those wishing to use radial basis functions should use Pysmo instead. New Capabilities MSContactor model for unit operations involving mass transfer between 2 or more streams, such as membrane, solvent extraction and solids leaching operations. Other Improvements Improved formulation for solubility products with additional parameters for better scaling of terms Better backward compatibility, verification and robustness testing of core models and APIs Added support for Separator models without energy balances

DiagnosticsToolbox↗

Band Engineering of Dirac Semimetals Using Charge Density Waves

New developments in the field of topological matter are often driven by materials discovery, including novel topological insulators, Dirac semimetals and Weyl semimetals. In the last few years, large efforts have been performed to classify all known inorganic materials with respect to their topology. Unfortunately, a large number of topological materials suffer from non-ideal band structures. For example, topological bands are frequently convoluted with trivial ones, and band structure features of interest can appear far below the Fermi level. This leaves just a handful of materials that are intensively studied. Finding strategies to design new topological materials is a solution. Here we introduce a new mechanism that is based on charge density waves and non-symmorphic symmetry to design an idealized Dirac semimetal. We then show experimentally that the antiferromagnetic compound GdSb 0.46 Te 1.48 is a nearly ideal Dirac semimetal based on the proposed mechanism, meaning that most interfering bands at the Fermi level are suppressed. Finally, its highly unusual transport behavior points to a thus far unknown regime, in which Dirac carriers with Fermi energy very close to the node seem to gradually localize in the presence of lattice and magnetic disorder.

36 MATERIALS SCIENCE↗

Mechanisms of paint bake response in resistance spot-welded first and third generation AHSS

Implementation of 3rd generation advanced high strength steels (3GAHSS) in automotive structures requires careful consideration of joining process implications. Due to the presence of increased carbon equivalent in 3GAHSS such as 980 HF relative to commonly-applied 1st generation AHSS such as 980 DP, the resultant properties of the weld nugget and heat affected zones in resistance spot welded must be engineered to provide consistent and acceptable performance, specifically in cross-tension loading mode. Although the as-welded cross-tension strength (CTS) of 980 HF is less than 980 DP, there is a significant improvement of the CTS after paint baking in 980 HF welds. 980 DP steel welds do not exhibit such marked improvement upon baking. The mechanism of the strong and beneficial effect of paint baking on 980 HF in comparison to 980 DP is discussed in light of its effect on residual stress distributions and microstructures. Although residual stress (strain) reduction is observed via synchrotron x-ray diffraction for all tested steels, this effect is demonstrated as secondary to the performance restoration of the weld joint in cross tension. High-resolution electron channeling contrast imaging (ECCI) micrographs reveal that paint baking affects a more beneficial degree of martensite tempering in 980 HF as compared to 980 DP. The martensite tempering is also evidenced by both a reduction in nano-hardness of critical microstructural features and re-emergence of ductile fracture behavior following the paint baking process. The tempering of martensite is concluded to be the dominant mechanism in improving cross tension strength of 3GAHSS welds following paint baking.

36 MATERIALS SCIENCE↗

Nonlinear Interface Reduction for Time-Domain Analysis of Hurty/Craig-Bampton Superelements with Frictional Contact

Virtual prototyping in engineering design relies today on modern numerical models of contacting structures with accurate resolution of interface mechanics, which strongly affect the system-level stiffness and energy dissipation due to frictional losses. High-fidelity modeling within the localized interfaces is required to resolve local quantities of interest that may drive design decisions. The high-resolution finite element meshes necessary to resolve inter-component stresses tend to be computationally expensive, particularly when the analyst is interested in response time histories. The Hurty/Craig-Bampton (HCB) transformation is a widely used method in structural dynamics for reducing the interior portion of a finite element model while having the ability to retain all nonlinear contact degrees of freedom (DOF) in physical coordinates. These models may still require many DOF to adequately resolve the kinematics of the interface, leading to inadequate reduction and computational savings. This study proposes a novel interface reduction method to overcome these challenges by means of system-level characteristic constraint (SCC) modes and properly orthogonal interface modal derivatives (POIMDs) for transient dynamic analyses. Both SCC modes and POIMDs are computed using the reduced HCB mass and stiffness matrices, which can be directly computed from many commercial finite element analysis software. Comparison of time history responses to an impulse-type load in a mechanical beam assembly indicate that the interface-reduced model correlates well with the HCB truth model. Localized features like slip and contact area are well-represented in the time domain when the beam assembly is loaded with a broadband excitation. The proposed method also yields reduced-order models with greater critical timestep lengths for explicit integration schemes.

42 ENGINEERING↗

Altermagnetic polar metallic phase in ultrathin epitaxially strained RuO 2 films

Altermagnetism refers to a wide class of magnetic orders featuring magnetic sublattices with opposite spins related by rotational symmetries, resulting in nontrivial spin splitting and magnetic multipoles. However, the direct observation of the altermagnetic transition remains elusive. Here, by combining theoretical analysis, electrical transport, X-ray, and optical spectroscopies, we establish a phase diagram in hybrid molecular beam epitaxy-grown RuO 2 /TiO 2 (110) films, mapping symmetries along with altermagnetic/electronic/structural phase transitions as functions of film thickness and temperature. This features an altermagnetic metallic polar phase in epitaxially strained 2 nm films, suggesting a potential link between polar metals and altermagnetic materials. Such a clear signature of a magnetic phase transition at ~500 K is observed exclusively in ultrathin strained films, unlike in bulk RuO 2 single crystals. These results highlight the power of epitaxial heterostructure engineering to induce altermagnetism in systems initially nonmagnetic, opening avenues for realizing emergent quantum phases with multifunctional properties.

RuO2 thin film↗

ComStock™ [SWR-19-33 and SWR-20-32]

ComStock™ is an analytic methodology for modeling the energy usage of the commercial building stock within the United States of America. The commercial building stock is represented through a sampling of complex probabilistic distributions of various features of interest for modeling energy usage within commercial buildings. Each sample from these distributions is converted into a building energy model based on the features of that specific sample. Each building energy model can be simulated as is, but additional changes can be made to the model through addition of energy conservation measures, component faults, or other desired alterations. The results of the simulations are then processed to provide insights for various stakeholders, including but not limited to policy makers, engineers, and marketers.

Horsey, Henry↗

ComStock™ 2024 Release 1 [SWR-19-33 and SWR-20-32]

ComStock™ is an NREL model of the U.S. commercial building stock. The model takes some building characteristics from the U.S. Department of Energy's (DOE's) Commercial Prototype Building Models and Commercial Reference Building. However, unlike many other building stock models, ComStock also combines these with a variety of additional public- and private-sector data sets. Collectively, this information provides high-fidelity building stock representation with a realistic diversity of building characteristics. This repository contains the source code used to build and execute ComStock models, including upgrade scenarios. In addition, the sampling of buildings characteristics used for the initial ComStock (V1.0) release is provided. The ComStock model is under active calibration and development, which is publicly visible on this repository. Execution of the ComStock workflow is managed through the buildstockbatch repository, a shared asset of ResStock™ and ComStock™ , specifically developed to scale to execution of tens of millions of simulations through multiple infrastructure providers. The dataset output from the initial ComStock (V1.0) release can be found at the accompanying ComStock data viewer website and additional information about ComStock found on the NREL Buildings Website. For more details about ongoing model development please consult the End Use Load Profiles website. ComStock is a direct result of the NREL residential stock modeling tool ResStock™ (recipient of a R&D100 award) and was inspired by the high-fidelity solar & storage adoption model dGen™. Additionally, this tool would not be possible without the decades of work undertaken by the OpenStudio® and EnergyPlus® visionaries and contributors, significant funding, feedback and support from the Los Angeles Department of Water and Power, and the Department of Energy's Building Technology Office ongoing support of and investment in building energy modeling software. is an analytic methodology for modeling the energy usage of the commercial building stock within the United States of America. The commercial building stock is represented through a sampling of complex probabilistic distributions of various features of interest for modeling energy usage within commercial buildings. Each sample from these distributions is converted into a building energy model based on the features of that specific sample. Each building energy model can be simulated as is, but additional changes can be made to the model through addition of energy conservation measures, component faults, or other desired alterations. The results of the simulations are then processed to provide insights for various stakeholders, including but not limited to policy makers, engineers, and marketers.

Horsey, Henry↗

Cybersecurity Standards, Certification, and Best Practices for DERs

Distributed energy resources (DERs) are becoming increasingly important to the electric grid, including solar energy systems. However, DERs also introduce new cybersecurity risks, including those posed by cloud computing. Standards harmonization is essential for ensuring that DERs are secure and can be safely integrated into the grid. This panel will discuss cyber standards harmonization for solar security. The panel will feature experts from the S2G Program, National Labs and Industry who will discuss the following topics: the cybersecurity risks and future benefits posed by ubiquitous solar energy systems, the development and implementation of cloud-based security solutions for DERs, including solar energy systems, the challenges and opportunities for harmonizing DER cybersecurity standards, and Cyber Informed Engineering and the solar security implementations The panel will also discuss the following specific initiatives: the S2G Program's DER Cybersecurity Framework, UL's DER Cybersecurity Certification Program, and IEEE 1547 Updates. The panel will conclude with a discussion of the future of standards harmonization for DER cybersecurity.

14 SOLAR ENERGY↗

Effect of Heat Treatment on Microstructure and Mechanical Property of 316L Stainless Steel Produced by Laser Powder Bed Fusion

The advanced non-light water reactor designs (Gen IV reactors), including molten salt/ very high temperature/ sodium-cooled and lead-cooled fast reactors, typically operate at higher temperatures and more extreme radiation conditions than light water reactors. An intrinsic part of the deployment and progress of Gen IV reactor designs is selecting the most suitable structural material for a specific application. Additive manufacturing (AM), a fairly new process of making physical, three-dimensional objects from a computer design file, is going to completely change the way of design, build and certify nuclear systems. It offers a range of opportunities to produce complex geometries from existing materials, offers new routes for processing of previously difficult to process materials, allows for design of new high-performance materials, and finally facilitates hybridization of dissimilar materials. This emerging technology has successfully produced cars, wind turbine blade molds and even live cells. It could also open up big opportunities for the nuclear industry to quickly deploy technologies at a fraction of the cost. So far, AM techniques have been preliminarily applied in the field of nuclear reactors, including the classical parts such as the pressure vessel of a small reactor with 508-III steel, the bottom nozzle of a fuel assembly with 304L steel, the fuel cladding with zirconium alloy and the integrated impeller of a pump and the multi-channel valve body with 316L steel [6,7]. The AM applications for operating nuclear reactors started in auxiliary plant components and have slowly migrated to metallic reactors and core components, but many of these are not safety critical components. Although many parts used for nuclear reactors have been fabricated by AM techniques, practical applications in engineering are still a long way off due to the uncertainty factors focused on the processing, material properties, analysis methods and application standards, which feeds the safety and life-cycle of the nuclear reactor. Due to rapid, repeated heating and cooling during production, a high dislocation density was present in the AM material. This microstructure feature is unstable at elevated temperature while high temperature is one of the typical operation environments for nuclear reactors. Thus, it is important to understand the thermal effect on the microstructure of AM material. The objectives of this study are to investigate the effect of heat treatment on the microstructure and mechanical properties of 316L stainless steel produced by laser powder bed fusion additive manufacturing, and to determine an appropriate heat treatment practice that will be applied to the lightweight AM lattice-structured material with the same chemistry. The heat treatment study consisted of annealing the samples at a temperature range of 800 to 1200 oC with a 50 oC increment for different times (1-24 hours), followed by vacuum or air cooling. Microstructural characterization was carried out by Scanning Electron Microscope (SEM). Grain size and crystallographic orientation were investigated by Electron Backscatter Diffraction (EBSD). Vickers hardness tests with a 0.5 kg load were employed to determine the hardness of samples after different heat treatments. After heat treatment, the random crystallographic orientation was preserved, and the volume fraction of high-angle grain boundaries (grain boundary misorientation =15 oC) remained the same. The dislocation density decreased with annealing temperature due to recovery. The fine subgrain structures in the as-printed specimen were quite stable up to 1200 oC. Minimal recrystallization was observed up to 1200 oC. Recrystallization initiated only after 8.5 hours at 1200 oC. The SEM images did not show obvious dependence of microstructure on cooling rate. The hardness of the specimens decreased with increasing annealing temperature as a result of the decrease in dislocation density. It is interesting to note that the AM material showed very similar hardness to the wrought material when annealing at similar temperature, although the microstructures are very different. Annealing at 1050 oC for 1 hour followed by air cooling was selected as the heat treatment procedure for the lattice designed lightweight AM 316L material.

36 MATERIALS SCIENCE↗

Library of Advanced Materials for Engineering (LAM) 4.56

Accurate and efficient constitutive modeling remains a cornerstone issue for solid mechanics analysis. Over the years, the LAME advanced material model library has grown to address this challenge by implementing models capable of describing material systems spanning soft polymers to stiff ceramics including both isotropic and anisotropic responses. Inelastic behaviors including (visco)plasticity, damage, and fracture have all incorporated for use in various analyses. This multitude of options and flexibility, however, comes at the cost of many capabilities, features, and responses and the ensuing complexity in the resulting implementation. Therefore, to enhance confidence and enable the utilization of the LAME library in application, this effort seeks to document and verify the various models in the LAME library. Specifically, the broader strategy, organization, and interface of the library itself is first presented. The physical theory, numerical implementation, and user guide for a large set of models is then discussed. Importantly, a number of verification tests are performed with each model to not only have confidence in the model itself but also highlight some important response characteristics and features that may be of interest to end-users. Finally, in looking ahead to the future, approaches to add material models to this library and further expand the capabilities are presented.

36 MATERIALS SCIENCE↗

Library of Advanced Materials for Engineering (LAMÉ) 4.58

Accurate and efficient constitutive modeling remains a cornerstone issue for solid mechanics analysis. Over the years, the LAMÉ advanced material model library has grown to address this challenge by implementing models capable of describing material systems spanning soft polymers to stiff ceramics including both isotropic and anisotropic responses. Inelastic behaviors including (visco)plasticity, damage, and fracture have all incorporated for use in various analyses. This multitude of options and flexibility, however, comes at the cost of many capabilities, features, and responses and the ensuing complexity in the resulting implementation. Therefore, to enhance confidence and enable the utilization of the LAMÉ library in application, this effort seeks to document and verify the various models in the LAMÉ library. Specifically, the broader strategy, organization, and interface of the library itself is first presented. The physical theory, numerical implementation, and user guide for a large set of models is then discussed. Importantly, a number of verification tests are performed with each model to not only have confidence in the model itself but also highlight some important response characteristics and features that may be of interest to end-users. Finally, in looking ahead to the future, approaches to add material models to this library and further expand the capabilities are presented.

36 MATERIALS SCIENCE↗