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At least 109 records · Page 6

An additively manufactured AlCuMnZr alloy microstructure and tensile mechanical properties

In this study, selective laser melting (SLM) was used to fabricate an AlCuMnZr alloy. The microstructural features that resulted from additive manufacturing (AM) were significantly refined compared to the corresponding cast alloy features. A combination of fine equiaxed and columnar grains along with in-situ formation of θ' precipitates during AM leads to enhanced yield strength (up to 300°C) in the as-fabricated AM alloy. The refinement of brittle intermetallics and a bimodal grain size distribution leads to improved tensile elongation in the AM alloy. The results illustrate the microstructural advantages that can result from additive processing over conventionally processed microstructures.

36 MATERIALS SCIENCE↗

Effects of transient thermal shock on the microstructures and corrosion properties of a reduced activation high-entropy alloy

The devices would subject transient thermal shocks (TTS) during operation under extremely harsh conditions of nuclear fusion reactors, which inevitably exert significant impact on the microstructure and performance of structural materials. Here, a reduced activation VCrFeTa 0.2 W 0.2 high-entropy alloy (HEA) was developed by vacuum arc melting. The effects of electron beam induced TTS on its microstructure, microhardness, and corrosion properties were investigated. The results indicate that the weight fraction of each phase changes after TTS, showing a significant decrease in the content of BCC1 phase and an increase in the content of BCC2 and Laves phases. The content of BCC1 phase continues to decrease slightly with increasing the power of TTS. Besides, the microhardness of the alloy increases from ~673 HV to ~714 HV after TTS treatments. In the reduced activation HEA, TTS results in a relatively low corrosion current density of ~0.472 μA/cm 2 in 3.5 wt% NaCl solution, around one-third of the current density observed in the as-cast sample. Furthermore, the VCrFeTa 0.2 W 0.2 HEA after TTS exhibits a pitting potential of ~1.165 V SCE , which is much higher than that of the as-cast sample. The refined composite multiscale entropy method is employed to analyze the influence of TTS on current fluctuation behavior during the corrosion process. The reduced activation VCrFeTa 0.2 W 0.2 HEA exhibits excellent properties in harsh environments after TTS, thereby showing advantageous property in the field of nuclear structural materials. Furthermore, TTS is an efficient and controllable strategy for the improvement of the HEAs’ microstructures and performances.

36 MATERIALS SCIENCE↗

High-pressure melt dynamics in shock-compressed titanium

In this work we study the high-pressure melting behavior of titanium using laser-driven shock compression with in situ femtosecond x-ray diffraction and molecular-dynamics simulations based on a machine-learned interatomic potential. The MD simulations predict the solid-liquid coexistence on the Hugoniot in the ∼111−124GPa range. Experimentally, we observe the first evidence of liquid at 86 GPa. We also observe pronounced microstructural changes with pressure, with strong grain refinement associated with the emergence of liquid, within the solid-liquid coexistence (∼110−126GPa). Above 126 GPa, we observe the persistence of residual levels of highly textured crystalline Ti to ∼180GPa, well above the expected melt completion pressure. We discuss the accuracy that current laser-shock experimental platforms have at determining the melt onset and completion pressures.

36 MATERIALS SCIENCE↗

Radioactive Material Dynamics @ NSLS-II [Slides]

RMD @ NSLS-II helps pave the path to a DMMSC: Developing expertise in techniques and experimental methods for DMMSC science; Improving capabilities for models to become microstructurally aware; Workforce training and development; Help refine DMMSC scientific requirements; Complementary to DMMSC XFEL science (EDXD/EXAFS)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Alloying effects on the microstructure and properties of laser additively manufactured tungsten materials

A large body of literature within the additive manufacturing (AM) community has focused on successfully creating stable tungsten (W) microstructures due to significant interest in their application for extreme environments. However, cracking and additional embrittling features at grain boundaries have resulted in poorly performing materials, stymying the application of AM as a manufacturing technique for W. Several alloying strategies, such as ceramic particles and ductile elements, have emerged with the promise to eliminate cracking while simultaneously enhancing stability against recrystallization. Here, in this work, we provide new insights regarding the defects and microstructural features that result from the introduction of ZrC for grain refinement and NiFe as a ductile reinforcement phase – in addition to the resulting thermophysical and mechanical properties. ZrC is shown to promote microstructural stability with increased hardness due to the formation of ZrO 2 dispersoids. Conversely, NiFe forms into micron-scale FCC phase regions within a BCC W matrix, producing enhanced toughness relative to pure AM W. A combination of these effects is realized in the WNiFe + ZrC system and demonstrates that complex chemical environments coupled with the tuning of AM microstructures provides an effective pathway for enabling laser AM W materials with enhanced stability and performance.

36 MATERIALS SCIENCE↗

Assessment of effective elastic constants of U-10Mo fuel: A multiscale modeling and homogenization study

The significant microstructural changes that U-Mo fuel undergoes during operation degrades its mechanical properties and structural integrity. Microstructural evolution entails the formation, evolution, and redistribution of porosity in conjunction with grain refinement. In the present paper, we employ numerical approaches to assess the impact of the various microstructural features—grains, nanoscale intragranular fission gas bubbles, and mesoscale intergranular voids—on the degradation of elastic constants. Phase-field microstructure models are combined with the asymptotic expansion homogenization technique in order to derive the effective elastic constants as a function of porosity and fission density. Here the results are verified and compared against theoretical bounds. Using this approach, elastic degradation in operating nuclear fuels can be quantified when the distributions of microstructural features are known.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Microstructural evolution in shear-punch tests: A comparative study of pure Cu and Cu-Cr alloy

Understanding the mechanisms behind microstructural evolution during shear deformation has been a long-standing area of interest. However, establishing a connection between microstructure, mechanical properties, and extent of shear deformation is challenging and requires refined experimental approaches. Shear-punch testing (SPT) provides a controlled method to introduce shear into small volumes of material that later can be subjected to detailed microstructural characterization. In this study, we utilize an SPT device to induce shear deformation to pure copper and a binary copper-chromium alloy. Electron backscatter diffraction and transmission electron microscopy were used to study the mechanisms of plastic deformation after SPT. Our results indicate that shear deformation of pure Cu produces a dense network of intercepting microshear bands upon sustained deformation. Twin boundaries undergo degradation into high angle grain boundaries due to simultaneous deviation from the axis-angle pair condition of 60° misorientation on [111] direction. The presence of 50% volume Cr particles in the soft Cu matrix fundamentally altered the shear deformation mechanism. Preferential deformation of the Cu matrix led to accelerated shear-induced formation of low and high angle grain boundaries, and subsequent grain refinement. Comparatively, no grain refinement occurred in pure Cu at a strain ~10 times larger (ϵ = 4.73) than that of the copper-chromium case (ϵ = 0.42). Overall, our study sheds light on the microstructural evolution during shear deformation and highlights the significant influence of particle reinforcements on the shear deformation mechanisms of metals.

36 MATERIALS SCIENCE↗

Influence of high-strain-rate compression and subsequent heat treatment on (TiNbZr) 89 (AlTa) 11 refractory high-entropy alloys: Dynamic-mechanical behavior and microstructural changes

This study explored the dynamic-mechanical behavior of a novel low-density (TiNbZr) 89 (AlTa) 11 refractory high-entropy alloy (RHEA) across strain rates ranging from 1.0×10 3 to 3.5×10 3 s –1 . A significant increase in the yield and ultimate compressive strengths with rising strain rates up to 3.0×10 3 s –1 was observed and attributed to enhanced dislocation activities and stress-induced microstructural transformations. The formation of the B2 phase and Zr 5 Al 3 precipitates was found to be crucial in bolstering the alloy strength at high strain rates. Beyond strain rates of 3.0×10 3 s –1 , a decrease in strength occurred due to thermal softening and strain localization. Microstructural analyses at 3.5×10 3 s –1 revealed grain refinement, the development of micro shear bands, and dislocation tangles, which were indicative of dynamic recrystallization. Besides, the findings also revealed that the post-dynamic compression heat treatment further enhanced the hardness and microstructural stability of the alloy. These results highlight the potential of the (TiNbZr) 89 (AlTa) 11 RHEA for applications requiring materials with high strength-to-weight ratios, particularly in dynamically loaded environments. It is expected that the results of this study will further advance our fundamental understanding of the behavior of RHEAs under extreme conditions, thereby opening new avenues for material innovation.

36 MATERIALS SCIENCE↗

Effects of secondary void-initiating particles on the steady-state crack growth resistance of high-strength steel

In this investigation, we focus on the dependence of stable crack growth resistance, as measured by the short-rod fracture toughness test, on secondary void-initiating particles such as AlN and Ti-based grain-refining precipitates in a variety of high-strength steels with tempered martensitic microstructures. The model developed by Ritchie and Thompson is modified to illustrate the significant amounts of toughening that can result from the refinement of secondary particles. Analysis of the data suggests that material strength is a predominant factor in increasing the short-rod fracture toughness relative to linear-elastic measures of initiation fracture toughness, but the extent of toughening is limited by the size and number density of secondary particles in the microstructure. The variation in estimates of secondary microvoid initiation and growth strains with precipitate size reinforce the notion that primary fracture at non-metallic inclusions and secondary fracture at smaller particles occur as sequential processes with a degree of concurrence that is dependent on the state of precipitation in both particle dispersions. Toughening in this connection is maximized by increases in microvoid growth strain that result from decreases in the size and areal number density of secondary void-initiating particles. Finally, the occurrence of transient instabilities during crack extension in short-rod specimens is explained with a phenomenological model that relates crack growth stability to natural variations in the dispersion of secondary void-initiating particles in the microstructure.

42 ENGINEERING↗

Benchmark microgravity experiments and computations for 3D dendritic-array stability in directional solidification

In this study, we present a comprehensive quantitative analysis of stability bands for dendritic arrays during directional solidification of a transparent succinonitrile-0.46 wt % camphor alloy, spanning a broad range of pulling velocities. Taking advantage of the microgravity environment aboard the International Space Station where most convection effects are suppressed, we obtain unique measurements that quantify the stable primary spacing range of spatially extended three-dimensional dendritic array structures under purely diffusive growth conditions. Through carefully designed velocity jump experiments and detailed examination of sub-grain boundary dynamics, we characterize key instabilities, including elimination and tertiary branching, shedding new light on the mechanisms governing dynamic dendritic spacing selection in extended 3D arrays. Phase field simulations are performed to characterize the stability limits of dendritic array structures for quantitative comparison with the flight experiments. Although the simulations capture general trends, significant deviations are noted at the upper stability boundary, indicating the influence of additional, unexplored factors. These findings contribute to a deeper understanding of dendritic growth dynamics and offer valuable benchmark data that could aid in refining predictive models and improving control of dendritic microstructures in metallurgical applications.

36 MATERIALS SCIENCE↗

Studies on the compositional dependent structural and electrical properties of CaTiO3-modified K0.5Na0.5NbO3 piezoelectric system

Lead-free piezoelectric ceramics of (1 − x)K0.5Na0.5NbO3-xCaTiO3 were fabricated, and their crystal structure, microstructure, and electrical properties were systematically studied. Rietveld refinement of the x-ray diffraction data and Raman spectroscopic analyses revealed a composition-dependent structural phase transition: three phase transitions, namely, from a pure orthorhombic phase for x ≤ 0.02 to a mixed phase of orthorhombic and tetragonal phases (0.03 ≤ x ≤ 0.08) and finally another mixed phase of tetragonal + cubic for x = 0.10 and 0.15 at room temperature (RT). The morphological study reveals a decrease in grain size along with a more uniform distribution of grains as the concentration of CaTiO3 (CT) increases; notably, a homogeneous distribution of grains is observed for x = 0.05. The temperature-dependent dielectric properties show two phase transitions, from orthorhombic to tetragonal (TO-T) and tetragonal to cubic (TC), for unmodified K0.5Na0.5NbO3 (KNN). However, both the phase transition temperatures (TO-T and TC) decrease, and the transition peaks broaden with an increase in CT substitution, and for x > 0.06, the TO-T shifted below RT. The broadening of the transition peak at TO-T may be due to the relaxation behavior. Among the prepared samples, the 5 mol. % CT-modified KNN shows the optimum electrical properties (d33 = 114 pC/N, ɛr = 412, and 2Pr = 15.25 μC/cm2) at RT. The enhanced electrical properties for x = 0.05 are due to the coexistence of orthorhombic and tetragonal phases, facilitating easy polarization rotation and flattening of the free energy profile. A phase diagram has been constructed based on the information gathered from the temperature-dependent dielectric measurements, RT x-ray diffraction, and Raman spectroscopy data and is discussed in detail.

Physics↗

Robust Dissimilar Metal Friction Welded Spool for Enhanced Capability for Steam Power Components (Final Program Report)

This project successfully demonstrated the feasibility and advantages of producing durable, friction-welded dissimilar-metal spools, both with and without transition pieces, as well as the use of advanced oxidation-protective coatings for steam power applications. The work encompassed the optimization and full-scale production of NFA tubing, overcoming manufacturing and processing challenges to achieve enhanced strength, creep, and fatigue properties validated by extensive microstructural characterization. Optimized welding techniques were developed and refined for joining dissimilar materials, resulting in defect-free welds optimized for both low- and high-pressure boiler circuits. Systematic evaluation of welding parameters, coupled with heat treatments, ensured reliable performance and minimized weld defects such as banding and cracking. Comprehensive mechanical and non-destructive testing, including tensile, bend, fatigue, and CT scanning, confirmed the superior integrity and durability of the friction-welded joints under representative service conditions. To address oxidation-related degradation, a range of protective alloy coatings—such as IN625, APMT, Duplex 2507, and FeCrAlY—were selected and evaluated for their ability to counteract oxide notch formation at dissimilar metal interfaces. These coatings demonstrated improved oxidation resistance and long-term stability under thermal cycling, thereby extending weld service life. Thermal cyclic testing and long-term studies captured the phase stability and diffusion behavior of coated and uncoated configurations. Validated models for low-cycle fatigue (LCF), creep, and thermal mechanical fatigue (TMF) were developed to predict component life and failure modes. These models confirmed that friction-welded configurations exhibited significantly enhanced performance compared to conventional gas-tungsten arc welding (GTAW), with up to 7× improvement in creep resistance and at least 2× enhancement in fatigue properties. The introduction of a tailored transition piece further reduced thermally induced strains, enhancing fatigue life. The results demonstrate a robust pathway for retrofitting existing steam fleet components and upgrading future equipment to deliver substantially improved cold-start cycling behavior and reduction of unplanned outages due to premature weld failures.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Enabling Real-time Scattering Data Analysis with Scalable Optimization [Slides]

Diffraction experiments produce datasets with rich multidimensional physics information such as microstructure, equations of state, crystal structure, elastoplastic properties, and other key inputs to LANL mission-essential multiphysics models. This information is typically extracted through a process called Rietveld refinement, which involves selecting appropriate models of the instrument, crystal structure, and microstructure, identifying suitable starting values, and then fitting often hundreds of model parameters using a sequence of empirical parameter turnon/off sequences within a non-global gradient-based optimization. Extensive user expertise is required to properly setup a refinement, identify appropriate models, and select initial parameter values close to truth, such that the refinement will yield parameter values that are optimally predictive. This is a very tedious manual process performed far after the beamline campaign has ended. As facilities have become capable of generating larger volumes of data, the limitation in throughput due to Rietveld refinement has led to a dramatic increase in unanalyzed data as opposed to an intended increase in new science. In our FY22 TED, we demonstrated an integrated toolset providing near real-time automated Rietveld analysis. If this toolset can be optimized to provide automated Rietveld analysis in real-time, this could alleviate the bottleneck in unanalyzed diffraction data, aid in decision-making during experiments, and increase efficiency of the facility.

74 ATOMIC AND MOLECULAR PHYSICS↗

High Density of Strong yet Deformable Intermetallic Nanorods Leads to an Excellent Room Temperature Strength-Ductility Combination in a High Entropy Alloy

This paper introduces a new microstructural template for high entropy alloys (HEAs), where the face centered cubic (FCC) complex concentrated solid solution is reinforced with a high density of strong, yet deformable, nanorods of an ordered multi-component intermetallic L12 compound. Thermodynamic modeling has been employed to design this HEA with a large L12 volume fraction. Thermo-mechanical processing by isothermal annealing of the conventionally processed bulk cold-rolled alloy directly at precipitation temperatures, has been applied to produce a high density of uniformly distributed L12 nanorods within refined FCC grains, resulting from concomitant recrystallization and discontinuous precipitation processes. The nanorod morphology of the discontinuous L12 product has been established from three-dimensional atom probe tomography. The refined grains result in a complete coverage of the microstructure with discontinuously precipitated intermetallic nanorods. This nanorod strengthened HEA exhibits an exceptionally high room temperature yield strength of ~1630 MPa, good tensile ductility of ~15%, and an ultimate tensile strength of ~1720 MPa. Furthermore, a single L12 phase alloy, melted based on the precipitate composition in the two-phase FCC + L12 HEA, exhibits very high compressive deformability and strain hardenability, unusual for ordered intermetallic compounds. These results open a new strategy for design of fine-grained microstructures strengthened via ordered intermetallic phases, exploiting the beneficial effects of discontinuous precipitation, for achieving very high room temperature tensile strengths while maintaining good ductility.

Gwalani, Bharat↗

Conversion of real-world aluminum scrap streams into high-performance Al–Mg–Si–Cu automotive alloys using shear assisted processing and extrusion

The conversion of post-consumer aluminum (Al) scrap into usable Al alloys without adding primary Al is challenging because of excess impurities. In this work, >99% post-consumer Twitch, used beverage cans (UBCs), and remelt scrap ingots (RSIs) were used as feedstock materials. As-cast and solution heat-treated feedstock billets were extruded using Shear Assisted Processing and Extrusion (ShAPE) at ~510°C, followed by press quenching. To explore the development of the microstructure, texture, and underlying mechanisms and how they contribute to the overall strengthening in as-extruded and artificially aged samples, scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) were used to collect microstructure and texture data. The enhanced strength and ductility were corroborated with the microstructural features and crystallographic texture. Simple shear $\textrm{A}/\bar{\textrm{A}}$, $\textrm{A}_1^*/\textrm{A} _2^*$ texture components along with weak $\textrm{C}$ and $\textrm{B}/\bar{\textrm{B}}$ texture components were formed during extrusion; the texture was strengthened after heat treatment. The refined second-phase particles helped to retain the deformed microstructure and texture. The contributions of dislocation and precipitate strengthening were maximized when billets were solution-heat-treated prior to extrusion. This is attributed to the formation of effective supersaturated solid solutions during the ShAPE process, which precipitate out during the peak age treatment. Overall, the highest yield strength of 305 MPa, ultimate tensile strength of 350 MPa, and elongation of 12% were achieved in artificially aged samples, which are comparable to those of Al 6082-T6.

Al alloy↗

Part-scale evolution of fine-scale microstructural heterogeneity in solid-state additive manufacturing

Current solid-state additive manufacturing methods, refined through costly and time-consuming trial and error, have spurred interest in computational models that replicate material behavior under typical thermomechanical conditions (e.g., strain-rate ~ 102 s−1). These models, however, struggle to capture time-dependent microstructural evolution. In this work, Additive Friction-Stir Deposition (AFSD) is used as a representative case study for part-scale quantification of microstructure evolution at a fine spatial resolution (200 μm) by examining a liquid-nitrogen-cooled stop-action build via energy-dispersive X-ray diffraction coupled with a multi-channel detector. These results inform modeling efforts by linking process asymmetry to stored plastic strain, residual elastic strain, and texture development, and unlike current state-of-the-art characterization methods (e.g., EBSD or neutron diffraction), this approach provides both the spatial resolution and collection efficiency necessary to quantify fine-scale microstructural heterogeneity over large component volumes. As such, this technique provides essential validation data for computational models, e.g., crystal plasticity, enabling future prediction of heterogeneous behavior in AFSD and other additive manufacturing processes.

Franz, Cole [ORNL] (ORCID:0000000213465881)↗

Multiphysics Meshfree Degradation Modeling of Energy Storage Materials with Kernel Enrichment

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. Reference: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

25 ENERGY STORAGE↗

Kernel Enriched Meshfree Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Laboratory of the Rockies (NLR), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. References: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

97 MATHEMATICS AND COMPUTING↗