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DOE OSTI2023

A Hybrid Domain Overlapping Method for Coupling System Thermal Hydraulics and CFD Codes

A hybrid multiscale coupling methodology based on a domain overlapping approach has been developed for coupling System Thermal Hydraulics (STH) and Computational Fluid Dynamics (CFD) codes. The method has been implemented between the modern STH code SAM and the CFD code NekRS, using the coupling tool Cardinal. The coupling aims to extend the STH code's applicability to scenarios where local momentum and energy transfers are important yet difficult for STH codes to capture, such as three-dimensional mixing. Two coupling strategies are implemented and compared: a hybrid domain overlapping method and the conventional domain decomposition method. Here, the strategies are applied to two closed-loop applications, and the present method shows superior stability behavior when compared to the domain decomposition method. Then, the present coupling method is validated against experimental data from a double T-junction experiment. The present STH/CFD coupling shows improved agreement with experimental data when compared to STH standalone simulations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Robust Molecular Predictive Methods for Novel Polymer Discovery and Applications

Polymeric materials are ubiquitous in modern society and they play an instrumental role in almost all industries, undoubtedly including the energy and environment sectors. Increased demand of energy and awareness to sustainability both necessitates the development of novel polymers with enhanced properties. Unfortunately, their structural and behavioral complexity render such discovery challenging and impeded. To address this problem, scientists are developing various computational modeling techniques and leveraging their power to depict the relationship between structural characteristics of polymers and their properties (such as rheological behaviors), and use such prediction to guide the design and syntheses of novel polymeric materials with enhanced performances. Unfortunately, predicting the relationships between polymer structure and composition with rheological properties via atomistic modeling is still a major challenge because of the extended time and length scales involved. Studying dynamic shear viscosity and linear viscoelasticity using molecular models requires capabilities that have been elusive, including representation of large molecular weight chains with an effective internal scale capable of describing entanglement, shear-rates that are in the s-1 scale with accurate quantitative stresses, and chemically-realistic combinations of both homogeneous and heterogeneous systems. Motivated by these unmet challenges, the overall technical objective of this DOE-STTR Phase II project is to develop robust molecular predictive methods for advanced polymer discovery and applications and especially for designing and demonstrating the “smart” polymer-based waterflooding enhanced oil recovery (EOR) process. In particular, we apply state-of-the-art molecular modeling methods developed by our academic partner, Materials Stimulation Center (MSC) at California Institute of Technology (Caltech), to facilitate and accelerate the experimental discovery processes. During the Phase I of this project, we had focused on development and demonstration of the molecular modeling methods to describe rheological properties of non-Newtonian polymer fluids, and to improve our fundamental understandings of shear-thickening mechanism and kinetics. In Phase II, we further apply the theoretical models to guide our experimental programs to improve our design of smart rheology modifier (SRM) polymers and their optimization for EOR. Specifically, we have three objectives in the Phase II study: (1) to further improve out computational modeling methods, coupling with the advanced machine learning algorithms; (2) to develop cost-effective and efficient SRM-flooding process suitable for EOR applications under typical reservoir conditions; and (3) to further explore the application of our molecular predictive models for innovative material discovery in other industrial applications. The recent development of our multiscale predictive framework allows the successful prediction of rheological properties from the chemical structure for polymers of experimentally relevant molecular weights, and provides an in-silico machine learning engine for screening novel compositions and structures with optimized non-Newtonian response, required for both shear-thinning and shear-thickening applications. Our framework provides: (1) procedures and tools for systematic coarsening from atomistic models and reverse mapping of coarse-grain models to atomistic, (2) unique ab initio methods to characterize the atomistic origin of colloidal and interfacial interactions and phenomena, (3) systematic structure and composition builders based on practical descriptors that drive rheological changes in polymer melts and diluted polymer mixtures, (4) a rheological properties engine capable of predicting viscosity in the zero-shear limit and under realistic dynamic conditions (for shear-rates commensurate with experiments) for large heterogeneous systems, (5) coarse-grain force fields with improved non-bond descriptions based on accurate quantum mechanics, (6) an in-silico screening machine learning engine that feeds from the systematic model builders to cover the descriptors search space, computes the rheological properties from converged trajectories spanning sub-milliseconds and ranks them for each structure/composition using an automated viscosity-vs-shear rate fitness function that can be tuned for shear-thickening, shear-thinning and other rheological responses.

02 PETROLEUM↗

DOE OSTI2020

Nonlinear ionization dynamics of hot dense plasma observed in a laser-plasma amplifier

Understanding the behaviour of matter under conditions of extreme temperature, pressure, density and electromagnetic fields has profound effects on our understanding of cosmologic objects and the formation of the universe. Lacking direct access to such objects, our interpretation of observed data mainly relies on theoretical models. However, such models, which need to encompass nuclear physics, atomic physics and plasma physics over a huge dynamic range in the dimensions of energy and time, can only provide reliable information if we can benchmark them to experiments under well-defined laboratory conditions. Due to the plethora of effects occurring in this kind of highly excited matter, characterizing isolated dynamics or obtaining direct insight remains challenging. High-density plasmas are turbulent and opaque for radiation below the plasma frequency and allow only near-surface insight into ionization processes with visible wavelengths. Here, the output of a high-harmonic seeded laser-plasma amplifier using eight-fold ionized krypton as the gain medium operating at a 32.8 nm wavelength is ptychographically imaged. A complex-valued wavefront is observed in the extreme ultraviolet (XUV) beam with high resolution. Ab initio spatio-temporal Maxwell–Bloch simulations show excellent agreement with the experimental observations, revealing overionization of krypton in the plasma channel due to nonlinear laser-plasma interactions, successfully validating this four-dimensional multiscale model. This constitutes the first experimental observation of the laser ion abundance reshaping a laser-plasma amplifier. The presented approach shows the possibility of directly modelling light-plasma interactions in extreme conditions, such as those present during the early times of the universe, with direct experimental verification.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Development and Validation of MALAMUTE model for Electric Field Assisted Sintering of Structural Materials

Fusion power plant designs feature extreme material performance requirements for structural material candidates. In addition to conventional alloys, more advanced composites and oxide dispersion strengthened (ODS) alloys are being explored, however, achieving the desired microstructures to maximize performance using traditional manufacturing methods can be challenging. The advanced manufacturing (AM) electric field-assisted sintering (EFAS) technique offers improved control over the final microstructure through higher heating and cooling rates and moderate pressures. Modeling and simulation tools show promise in elucidating the process-structure-property-performance (PSPP) correlation for AM-produced parts, including the EFAS process. An inherently multiscale process, the EFAS technique aligns well with the multiscale modeling capability of the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE)[cite]. We present here an electro-thermo-mechanical approach to modeling the EFAS process using the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE) code. Prediction of the field and gradient distributions across the EFAS tooling is required to accurately describe the conditions for the lower-scale microstructural evolution models. In this work we present the MALAMUTE model developed to predict the electrical potential, temperature, and mechanical stress distribution across the EFAS graphite tooling and part at the larger engineering-scale. Validation of the MALAMUTE engineering-scale model is completed using data from experimental densification and pre-densified runs of iron powder via EFAS at 1000oC. These runs were conducted using a Thermal Technology DCS-5 EFAS system. Data collected during the experiment runs include the direct current (DC) supplied to the graphite tooling, the temperature of the graphite tooling as measured with a pyrometer, and the force applied to the top of the graphite tooling stack, and the data were recorded every 10 seconds. Our validation approach used the current and force data from the EFAS run as boundary condition inputs to the MAMALUTE simulation; the temperature data were used to evaluate the MALAMUTE EFAS model prediction. Results of the MALAMUTE simulations are employed to connect the external pyrometer temperature measurement to the temperature profile across the part undergoing consolidation. We investigate the impact of material property variation and mesh deformation on the temperature profile as predicted by MALAMUTE. We conclude by highlighting projects where the MALAMUTE EFAS modeling and simulation capabilities will be used to assist experimental design.

36 - MATERIALS SCIENCE↗

DOE OSTI2022

Elucidating the Initial Steps in α-Uranium Hydriding Using First-Principles Calculations

Hydrogen embrittlement of uranium, which arises due to the formation of a structurally weak pyrophoric hydride, poses a major safety risk in material applications. Previous experiments have shown that hydriding begins on the top or near the surface (i.e., subsurface) of α-uranium. However, the fundamental molecular-level mechanism of this process remains unknown. Here, in this work, starting from pristine α-U bulk and surfaces, we present a systematic investigation of possible mechanisms for the formation of metal hydride. Specifically, we address this problem by examining the individual steps of hydrogen embrittlement, including surface adsorption, subsurface absorption, and the interlayer diffusion of atomic hydrogen. Furthermore, by examining these processes across different facets, we highlight the importance of both (1) hydrogen monolayer coverage and (2) applied tensile strain on hydriding kinetics. Taken together, by studying previously overlooked phenomena, this study provides foundational insights into the initial steps of this overall complex process. We anticipate that this work will guide near-term future development of multiscale kinetic models for uranium hydriding and subsequently identify potential strategies to mitigate this undesired process.

36 MATERIALS SCIENCE↗

NASA NTRS2016

Agile Multi-Scale Decompositions for Automatic Image Registration

In recent works, the first and third authors developed an automatic image registration algorithm based on a multiscale hybrid image decomposition with anisotropic shearlets and isotropic wavelets. This prototype showed strong performance, improving robustness over registration with wavelets alone. However, this method imposed a strict hierarchy on the order in which shearlet and wavelet features were used in the registration process, and also involved an unintegrated mixture of MATLAB and C code. In this paper, we introduce a more agile model for generating features, in which a flexible and user-guided mix of shearlet and wavelet features are computed. Compared to the previous prototype, this method introduces a flexibility to the order in which shearlet and wavelet features are used in the registration process. Moreover, the present algorithm is now fully coded in C, making it more efficient and portable than the MATLAB and C prototype. We demonstrate the versatility and computational efficiency of this approach by performing registration experiments with the fully-integrated C algorithm. In particular, meaningful timing studies can now be performed, to give a concrete analysis of the computational costs of the flexible feature extraction. Examples of synthetically warped and real multi-modal images are analyzed.

Science Data Processing↗

NASA NTRS2016

Agile Multi-Scale Decompositions for Automatic Image Registration

Science Data Processing↗

NASA NTRS2017

Conjunction Assessment Techniques and Operational Results from the Magnetospheric Multiscale Mission

This paper will describe the results that have been obtained to date during the MMS mission concerning conjunction assessment. MMS navigation makes use of a weak-signal GPS-based system: this allows signals to be received even when MMS is flying above the GPS orbits, producing a highly accurate determination of the four MMS orbits. This data is downlinked to the MMS Mission Operations Center (MOC) and used by the Flight Dynamics Operations Area (FDOA) for both maneuver design and conjunction assessment. The MMS fly in tetrahedron formations around apogee, in order to collect simultaneous particles and fields science data. The original plan was to fly tetrahedra between 10 and 160 km in size; however, after Phase 1a of the mission, the science team requested that smaller sizes be flown if feasible. After analysis (to be detailed in a companion paper), a new minimum size of 7 km was decided upon. Flying at this reduced scale size makes conjunction assessment between the MMS spacecraft even more important: the methods that are used by the MMS FDOA to address this problem will be described in the paper, and a summary given of the previous analyses that went into the development of these techniques. Details will also be given of operational experiences to date. Finally, two CA mitigation maneuver types that have been designed (but never yet required to actually be performed) will also be outlined.

conjunction Assessment↗

DOE OSTI2021

Multiscale Structural Characterization of a Smectic Liquid Crystalline Elastomer upon Mechanical Deformation Using Neutron Scattering

Liquid crystalline elastomers (LCEs) exhibit unique shape memory behavior due to the combination of liquid crystalline orientation and rubber elasticity. Multiscale structural characterization of these materials upon deformation is crucial to understanding their structure–property relationships. In this work, the structure evolution of an epoxy-based, main-chain LCE with deuterated flexible spacers upon uniaxial mechanical deformation is investigated at different length scales. Wide-angle and small-angle X-ray scattering (WAXS/SAXS) reveal the presence of smectic polymorphism and rotations of the smectic domains upon mechanical stretching, which is also confirmed by small-angle neutron scattering (SANS). Importantly, the selective deuteration enables an improved neutron scattering contrast between the smectic and amorphous domains. SANS patterns of the deformed, deuterated LCE exhibit strong scattering streaks that are not observed in SAXS or SANS of hydrogenated LCE, indicating the presence of highly aligned amorphous domains. The macroscopic orientation also results in the formation of structures in the micrometer scale revealed by the ultrasmall-angle neutron scattering (USANS) experiment.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Vertically Resolved Analysis of the Madden-Julian Oscillation Highlights the Role of Convective Transport of Moist Static Energy

We simulate the Madden-Julian oscillation (MJO) over an aquaplanet with uniform surface temperature using the multiscale modeling framework (MMF) configuration of the Energy Exascale Earth System Model (E3SM-MMF). The model produces MJO-like features that have a similar spatial structure and propagation behavior to the observed MJO. To explore the processes involved in the propagation and maintenance of these MJO-like features, we perform a vertically resolved moist static energy (MSE) analysis for the MJO (Yao et al., 2022, https://doi.org/10.1175/jas-d-20-0254.1). Unlike the column-integrated MSE analysis, our method emphasizes the local production of MSE variance and quantifies how individual physical processes amplify and propagate the MJO's characteristic vertical structure. We find that radiation, convection, and boundary layer (BL) processes all contribute to maintaining the MJO, balanced by the large-scale MSE transport. Furthermore, large-scale dynamics, convection, and BL processes all contribute to the propagation of the MJO, while radiation slows the propagation. Additionally, we perform mechanism-denial experiments to examine the role of radiation and associated feedbacks in simulating the MJO. We find that the MJO can still self-emerge and maintain its characteristic structures without radiative feedbacks. This study highlights the role of convective MSE transport in the MJO dynamics, which was overlooked in the column-integrated MSE analysis.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

3.0 - MOOSE: Enabling massively parallel multiphysics simulations

The development of MOOSE has kept accelerating since the last release, with over 2,100 pull requests merged over the last 30 months that involved nearly fifty contributors across close to a dozen institutions internationally. The growth in MOOSE's capabilities and downstream applications is reflected in the growth of the community. User support provided on the GitHub discussions forum has steadily increased to nearly 50 daily interactions. New simulation projects, notably to model advanced nuclear reactor and fusion devices, are driving a significant expansion of the capabilities. This paper reports on these developments, with several major released features, new physics modules, and key improvements to the user experience and simulation workflow.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2016

Performance of the Goddard Multiscale Modeling Framework with Goddard Ice Microphysical Schemes

The multiscale modeling framework (MMF), which replaces traditional cloud parameterizations with cloud-resolving models (CRMs) within a host atmospheric general circulation model (GCM), has become a new approach for climate modeling. The embedded CRMs make it possible to apply CRM-based cloud microphysics directly within a GCM. However, most such schemes have never been tested in a global environment for long-term climate simulation. The benefits of using an MMF to evaluate rigorously and improve microphysics schemes are here demonstrated. Four one-moment microphysical schemes are implemented into the Goddard MMF and their results validated against three CloudSat/CALIPSO cloud ice products and other satellite data. The new four-class (cloud ice, snow, graupel, and frozen drops/hail) ice scheme produces a better overall spatial distribution of cloud ice amount, total cloud fractions, net radiation, and total cloud radiative forcing than earlier three-class ice schemes, with biases within the observational uncertainties. Sensitivity experiments are conducted to examine the impact of recently upgraded microphysical processes on global hydrometeor distributions. Five processes dominate the global distributions of cloud ice and snow amount in long-term simulations: (1) allowing for ice supersaturation in the saturation adjustment, (2) three additional correction terms in the depositional growth of cloud ice to snow, (3) accounting for cloud ice fall speeds, (4) limiting cloud ice particle size, and (5) new size-mapping schemes for snow and graupel. Despite the cloud microphysics improvements, systematic errors associated with subgrid processes, cyclic lateral boundaries in the embedded CRMs, and momentum transport remain and will require future improvement.

snow↗

DOE OSTI2025

Data for Unraveling the Drivers of Water Shortage across Spatial Scales and Sectors in Colorado's West Slope River Basins

Results from Sunkara et al. submitted to Earth's Future. All code to reproduce the experiment and make the figures can be found here: https://github.com/ssaiveena/Sunkara-etal_2025_WestSlope For a detailed guide to data in this repository, see the README.txt file. Shortage output from .xdd files generated by StateMod was compressed into .parquet files in the Uncertain_scenarios folder. Reservoir output from .xre files can be found in the "Reservoir" directory within the Uncertain_scenarios folder. We adopted the CDSS naming convention: cm = Upper Colorado River Basin gm = Gunnison River Basin ym = Yampa River Basin wm = White River Basin sj = Southwest Basin

Climate Change↗

DOE OSTI2020

Metallization of diamond

Experimental discovery of ultralarge elastic deformation in nanoscale diamond and machine learning of its electronic and phonon structures have created opportunities to address new scientific questions. Can diamond, with an ultrawide bandgap of 5.6 eV, be completely metallized, solely under mechanical strain without phonon instability, so that its electronic bandgap fully vanishes? Through first-principles calculations, finite-element simulations validated by experiments, and neural network learning, we show here that metallization/demetallization as well as indirect-to-direct bandgap transitions can be achieved reversibly in diamond below threshold strain levels for phonon instability. We identify the pathway to metallization within six-dimensional strain space for different sample geometries. We also explore phonon-instability conditions that promote phase transition to graphite. These findings offer opportunities for tailoring properties of diamond via strain engineering for electronic, photonic, and quantum applications.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Study on the Carbon Nanostructures for Nanosized Si Electrodes

Silicon (Si) has been considered as a next-generation anode material due to natural abundance, low operating potential (<0.5 V vs. Li/Li+), and high theoretical specific capacity of 4200 mAh g-1.[1] However, the electrochemical alloying reaction of Si involves large volume changes of 400% during lithiation and delithiation, causing cracking and pulverization of Si.[1] In addition, solid electrolyte interface (SEI) of Si anode experiences constant changes due to unstable SEI reactivity.[2] Considerable efforts have been made to design nanostructured Si materials to address the issues because nanostructuring can relieve the mechanical strain.[3] However, when compared to micrometer-sized active materials having sufficient electrolyte pathway through interparticle space, the nanoparticle (NP)-based electrodes tend to be densely packed. As mass loading is higher and electrode is thicker, ion transport issue can become more severe in the densely packed electrodes.[4] In this work, we will present studies on engineered porosity impacts performance in Si NP electrodes by altering carbon nanostructures. We explore the extreme limit of effectively non-porous electrodes using quasi-spherical, Si NPs, which result in densely packed electrodes when slurry is prepared with conventional carbon black. We engineer porosity using carbon nanostructures including multi-walled carbon nanotubes and carbon nanorods in place of conventional carbon black to create pore structure in Si NP-based electrodes. These experiments provide a correlation between mass loading, porosity and silicon utilization in Si NP-based electrodes. References: [1] C. K. Chan, H. Peng, G. Liu, K. Mcllwrath, X. F. Zhang, R. A. Huggins, Y. Cui, "High-performance lithium battery anodes using silicon nanowires", Nat. Nanotechnol., 2008, 3, 31, [2] J. D. McBrayer, M.-T. F. Rodrigues, M. C. Schulze, D. P. Abraham, C. A. Apblett, I. Bloom, G. M. Carroll, A. M. Coclasure, C. Fang, K. L. Harrison, G. Liu, S. D. Minteer, N. R. Neale, G. M. Veith, C. S. Johnson, J. T. Vaughey, A. K. Burrel, B. Cunningham, "Calendar aging of silicon-containing batteries", Nat. Energy, 2021, 6, 1164, [3] H. Wu, G. Zheng, N. Liu, T. J. Carney, Y. Yang, Y. Cui, "Engineering Empty space between Si Nanoparticles for Lithium-Ion Battery Anodes", Nano Lett., 2012, 12, 904, [4] X. Zhang, Z. Ju, Y. Zhu, K. J. Takeuchi, E. S. Takeuchi, A. C. Marschilok, G. Yu, "Multiscale Understanding and Architecture Design of High Energy/Power Lithium-Ion Battery Electrodes", Adv. Energy Mater., 2021, 11, 2000808

carbon nanostructure↗

DOE OSTI2022

High temperature stability and transport characteristics of hydrogen in alumina via multiscale computation

Here, the impact of hydrogen charge states on the stability and transport characteristics of hydrogen interstitials in alumina polymorphs is evaluated by multiscale computational methods including density functional theory (DFT), ab initio molecular dynamics (AIMD) and machine learned force fields. Thermodynamic calculations show that the protonic H i +1 interstitial is the most stable defect species for most values of the electronic bandgap in both and amorphous alumina (Al 2 O 3 ). Further, active learned Gaussian approximation potentials (GAP) were developed using AIMD data to study temperature dependent long time proton diffusion in alumina. Diffusivity calculations from GAP-MD simulations are found to be comparable with of the AIMD data, while being ~340 times faster and scalable to larger systems. Comparisons with diffusivity values for other interstitial charge states (H i 0 and H i -1 ) and published experimental literature indicate that H i +1 diffusion is the likely mechanism of hydrogen transport. A good agreement is obtained between H i +1 diffusivity calculated in α-Al 2 O 3 from DFT: 5.05 10 -3 exp(-0.81 eV/k B /T) cm 2 /s and reported experiment: 9.7X10 -4 exp(-0.83 eV/k B /T) cm 2 /s. Computationally and experimentally calculated energy barriers (0.81 and 0.83 eV respectively) only differ by 2.5%. Similarly, the pre-exponential diffusion coefficients only differ by 0.5 orders of magnitude. Moreover, the diffusivity of H i +1 in amorphous Al 2 O 3 in the 1000–2000 K range is calculated to be 2.53X10 -2 exp(-0.89 eV/k B /T), just one order of magnitude higher than the corresponding value in α-Al 2 O 3 . This suggests that local structural disorder does not significantly affect the energy landscape and diffusion behavior of H i +1 in Al 2 O 3 . Overall, these results show promise for the application of alumina polymorphs as hydrogen permeation barriers.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTi⁢O3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2009

A Continuum-Atomistic Analysis of Transgranular Crack Propagation in Aluminum

A concurrent multiscale modeling methodology that embeds a molecular dynamics (MD) region within a finite element (FEM) domain is used to study plastic processes at a crack tip in a single crystal of aluminum. The case of mode I loading is studied. A transition from deformation twinning to full dislocation emission from the crack tip is found when the crack plane is rotated around the [111] crystallographic axis. When the crack plane normal coincides with the [112] twinning direction, the crack propagates through a twinning mechanism. When the crack plane normal coincides with the [011] slip direction, the crack propagates through the emission of full dislocations. In intermediate orientations, a transition from full dislocation emission to twinning is found to occur with an increase in the stress intensity at the crack tip. This finding confirms the suggestion that the very high strain rates, inherently present in MD simulations, which produce higher stress intensities at the crack tip, over-predict the tendency for deformation twinning compared to experiments. The present study, therefore, aims to develop a more realistic and accurate predictive modeling of fracture processes.

Yamakov, V.↗