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969 records · Page 40

Detecting thermodynamic phase transition via explainable machine learning of photoemission spectroscopy

Identifying thermodynamic signatures of electronic phases, such as superconductivity, is challenging in low-dimensional materials due to strong fluctuations and low probing volume. Spectroscopic methods are often used to identify new bulk phases, but their main measurable quantity—electronic energy gaps—is no longer an effective order parameter in low-dimensional and fluctuating systems. Combining angle-resolved photoemission with a domain-adversarial neural network, we report a data-driven method to identify thermodynamic phase transitions solely based on single-particle spectra. We demonstrate 97.6% accuracy in cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+δ with strong superconducting fluctuations. This model notably compensates for the scarcity of experimental data by leveraging virtually inexhaustible simulated data. Further, its explainability reveals the crucial role of in-gap spectral weight in detecting phase fluctuations and thermodynamic transitions. Our work pinpoints the spectroscopic signatures of fluctuating orders and enables using spectroscopy for machine-learning-assisted material discovery for low-dimensional and strong coupling systems.

2D materials

Stationary Testing of a Pulse Tube Cryocooler Designed to Rotate at 6800 RPM with the Superconducting Rotor of an Electric Machine

Electrified aircraft are being developed to increase the efficiency and reduce the cost of operating subsonic transport aircraft. Achieving a substantial impact necessitates focusing on single- and twin-aisle aircraft which use propulsion systems with >20 MW ratings. For these aircraft, multi-MW superconducting electric machines are being developed due to their high specific power and high efficiency. Most of these electric machines employ superconductors on their rotor, thereby requiring cryogenic cooling of the rotating system. An attractive solution is to conductively cool the rotor using a cryocooler that rotates with the rotor. NASA has been developing a 50 K pulse tube cryocooler for its High Efficiency Megawatt Motor (HEMM) that can operate while rotating at up to 6,800 rpm. The first non-rotating tests of the fully assembled HEMM cryocooler have been completed, and initial testing has yielded a no-load temperature of 112 K. A small helium leak into the vacuum system has been identified as the major bottleneck to performance, and based on measurements with the motor turned off there is an observed vacuum-side heat leak of approximately 30 W at 115 K. Immediate next steps for testing are to locate and mitigate the apparent helium leaks into the vacuum chamber. Thus far, compressor performance and the apparent heat lift after correcting for the heat leak are on par with expectations.

Electrified Aircraft Propulsion

A novel digital lifecycle for Material‐Process‐Microstructure‐Performance relationships of thermoplastic olefins foams manufactured via supercritical fluid assisted foam injection molding

Abstract This research significantly enhances the applicability of thermoplastic olefins (TPOs) in the automotive industry using supercritical N 2 as a physical foaming agent, effectively addressing the limitations of traditional chemical agents. It merges experimental results with simulations to establish detailed material‐process‐microstructure‐performance (MP2) relationships, targeting 5–20% weight reductions. This innovative approach labeled digital lifecycle (DLC) helps accurately predict tensile, flexural, and impact properties based on the foam microstructure, along with experimentally demonstrating improved paintability. The study combines process simulations with finite element models to develop a comprehensive digital model for accurately predicting mechanical properties. Our findings demonstrate a strong correlation between simulated and experimental data, with about a 5% error across various weight reduction targets, marking significant improvements over existing analytical models. This research highlights the efficacy of physical foaming agents in TPO enhancement and emphasizes the importance of integrating experimental and simulation methods to capture the underlying foaming mechanism to establish material‐process‐microstructure‐performance (MP2) relationships. Highlights Establishes a material‐process‐microstructure‐performance (MP2) for TPO foams Sustainably produces TPO foams using supercritical (ScF) N 2 with 20% lightweighting Shows enhanced paintability for TPO foam improved surface aesthetics Digital lifecycle (DLC) that predicts both foam microstructure and properties DLC maps process effects & microstructure onto FEA mesh for precise prediction

Engineering

Study of wrap mode impact on Pseudomonas aeruginosa motion in the chemotactic field of fungi

An agent-based discrete computational model biologically calibrated to Pseudomonas aeruginosa migration is used to explore the impacts of bacterial reversals and wrap mode on the efficiency of motion in different environments, both with and without chemotaxis. It is first shown that wrap mode increases the exploration of continuous multimodal chemotactic profiles such as those produced by biologically relevant fungal networks. For cells undergoing a run-reverse pattern, it is shown that the bacteria are likely to remain at the first local chemoattractant maximal production site on a hypha they find. However, with wrap mode, the bacteria can more easily escape these local sites to further explore their neighboring environment along the fungi, suggesting that wrap mode may be beneficial for migration along the fungi in liquid. In a different set of simulations of bacterial motion close to an isolated chemotactic source, wrap mode is shown to increase the ability of a bacterium to reorient toward the source while reducing the overall motion required for similar chemotactic efficiency as a run-reverse strategy, suggesting a potential metabolic benefit. In contrast, model simulations show that wrap mode can increase the rate of dispersal of P. aeruginosa in a nonchemotactic environment.

Hansen, Austin [University of California, Riversid

A Kinetic Model of the Long-Term Corrosion of Glass-Ceramic Materials

Multiphase waste forms show promise for increased waste loading and for the ability to dispose of contaminated solid and particulate waste through direct densification. However, achieving predictive capability for long-term durability of multiphase waste forms, and thus assessing their possible deployment, requires expanding the current, limited knowledge base. Here, we describe the development of a corrosion model of a two-phase waste form consisting of crystals of known volume fraction embedded in a glass matrix. This model accounts for the dissolution of both the crystalline and glass phases as well as the hydration of the glass phase through an ion exchange reaction. Because of the large difference in solubility between the two phases, the reactive surface of the crystalline phase is a function of the extent of dissolution of the glass phase in this model. Model parameterization was performed using corrosion data, such as from single-pass flow-through tests, for the individual phases. The parameterized corrosion model was evaluated against static dissolution test data for a glass-ceramic multiphase waste form. This evaluation demonstrated the model’s ability to reproduce the time-dependent release of key tracers of glass and crystalline phase dissolution. Hence, the development of a kinetic model provides a pathway for long-term durability predictions and thus the use of multiphase waste forms in nuclear cleanup missions.

Kerisit, Sebastien N.

Unveiling the lithium-ion transport mechanism in Li{sub 2}ZrCl{sub 6} Solid-State Electrolyte {ital via} deep learning-accelerated molecular dynamics simulations.

Lithium zirconium chlorides (LZCs) present a promising class of cost-effective solid electrolytes for next-generation all-solid-state batteries. The unique crystal structure of LZCs plays a crucial role in facilitating lithium-ion mobility, which further affects the electrochemical performance. To understand the underlying mechanism governing ion transport, we employed deep learning-accelerated molecular dynamics simulation on Li2ZrCl6 (trigonal alpha- and monoclinic beta-LZC), focusing specifically on the zirconium coordination environment. Our results reveal that disordered alpha-LZC exhibits the highest ionic conductivity, while beta-LZC demonstrates significantly lower conductivity, closely aligning with experimental findings. The study confirms that across all phases, lithium migration proceeds via the site-to-site hopping mechanism, where variations in site residence times critically impact the overall ionic conductivity. In alpha-LZCs, lithium ions prefer to anisotropically diffuse across interlayers as the result of a lower energy barrier, driven primarily by collective diffusion. In contrast, lithium ions in beta-LZC primarily isotropically diffuse within the intralayer, hindered by higher energy barriers and determined by individual diffusion. The variation in ZrCl6 2- octahedral unit softening, induced by the specific layered arrangement of zirconium atoms, emerges as a critical determinant of the energy barriers across the LZC phases. These atomic-scale insights into the transport processes provide valuable guidance for the rational design and optimization of LZCs-based electrolytes, accelerating their practical application in advanced energy storage technologies.

Guo, Hanzeng

Battery Failure Databank

The Battery Failure Databank contains thermal runaway results gathered from nearly 300 small format fractional thermal runaway calorimetry (S-FTRC) experiments. A majority of these experiments were conducted at synchrotron facilities where high-speed x-ray videography was conducted of the cell while tested inside of the S-FTRC. The databank is a two-component system which consists of a Microsoft ExcelTM spreadsheet which provides S-FTRC results in tabular format and a radiographic video library containing the high-speed x-ray videos. Overall, the databank provides thermal results from S-FTRC experiments conducted on a mixture of commercially available lithium-ion (Li-ion) cells and specialized Li-ion test cells with varying cell format (18650, 21700, and D-cell) and trigger mechanism (heaters, heaters plus internal short circuiting device, and nail penetration). The radiography video component provides insight into the initiation and propagation of TR in the cells, in addition to consequences of TR measured by the FTRC. Fractions of mass ejected for the cell types are separated into regimes based on the different failure modes of the cells, such as purely venting, partial ejection, and total ejection. With knowledge of the rate and characterization of the internal degradation of the cells during TR, and the amounts of mass ejected and unrecovered, the extent of TR, and therefore the mitigation of TR, is revealed relative to cell types and failure modes.

Lithium-ion battery

Resonant Metasurfaces with Van Der Waals Hyperbolic Nanoantennas and Extreme Light Confinement

This work reports on a metasurface based on optical nanoantennas made of van der Waals material hexagonal boron nitride. The optical nanoantenna made of hyperbolic material was shown to support strong localized resonant modes stemming from the propagating high-k waves in the hyperbolic material. An analytical approach was used to determine the mode profile and type of cuboid nanoantenna resonances. An electric quadrupolar mode was demonstrated to be associated with a resonant magnetic response of the nanoantenna, which resembles the induction of resonant magnetic modes in high-refractive-index nanoantennas. The analytical model accurately predicts the modes of cuboid nanoantennas due to the strong boundary reflections of the high-k waves, a capability that does not extend to plasmonic or high-refractive-index nanoantennas, where the imperfect reflection and leakage of the mode from the cavity complicate the analysis. In the reported metasurface, excitations of the multipolar resonant modes are accompanied by directional scattering and a decrease in the metasurface reflectance to zero, which is manifested as the resonant Kerker effect. Van der Waals nanoantennas are envisioned to support localized resonances and can become an important functional element of metasurfaces and transdimensional photonic components. By designing efficient subwavelength scatterers with high-quality-factor resonances, this work demonstrates that this type of nanoantenna made of naturally occurring hyperbolic material is a viable substitute for plasmonic and all-dielectric nanoantennas in developing ultra-compact photonic components.

Chemistry

Molecular origin of anisotropic shear elastoplasticity in chitin

Chitin nano- and mesoscale structures present in the exoskeleton of crustaceans exhibit exceptional longitudinal stiffness and toughness, rivaling or even exceeding that of many synthetic polymer architectures. Here, we reveal the origin of the asymmetric shear response in chitin multiscale architectures, marked by pronounced anisotropy in deformation. Under shear aligned with the molecular axis, chitin accommodates strain through coherent atomic rearrangements that enable elastic recovery. In contrast, shear applied perpendicular to this axis induces liquid-like plasticity via localized sliding. These results demonstrate the intrinsic mechanical anisotropy of chitin, underpinning a dual function in resisting repetitive loading while dissipating internal stress during high-strain events. Our findings establish the molecular basis of shear elastoplasticity in multiscale chitin structures, wherein axial elasticity supports energy storage in load-bearing regions, whereas transverse plasticity enables controlled energy dissipation. These atomic-scale insights lay a foundation for the predictive design of chitin-based materials with tunable strength-toughness profiles.

Wan, Zhangmin [University of British Columbia, Van

Mechanically and Thermally Robust Gel Electrolytes Built from A Charged Double Helical Polymer

Polymer electrolytes have received tremendous interest in the development of solid-state batteries, but often fall short in one or more key properties required for practical applications. Herein, a rigid gel polymer electrolyte prepared by immobilizing a liquid mixture of a lithium salt and poly(ethylene glycol) dimethyl ether with only 8 wt% poly(2,2′-disulfonyl-4,4′-benzidine terephthalamide) (PBDT) is reported. The high charge density and rigid double helical structure of PBDT lead to formation of a nanofibrillar structure that endows this electrolyte with stronger mechanical properties, wider temperature window, and higher battery rate capability compared to all other poly(ethylene oxide) (PEO)-based electrolytes. The ion transport mechanism in this rigid polymer electrolyte is systematically studied using multiple complementary techniques. Li/LiFePO 4 cells show excellent capacity retention over long-term cycling, with thermal cycling reversibility between ambient temperature and elevated temperatures, demonstrating compelling potential for solid-state batteries targeting fast charging at high temperatures and slower discharging at ambient temperature.

36 MATERIALS SCIENCE

Novel additive manufacturing for plasma facing materials ‐ creating a research pathway for minority students

This project addresses two critical and intertwined challenges in fusion energy, namely the shortage of a broadly trained scientific workforce and the lack of scalable manufacturing solutions for plasma-facing components (PFCs). Through a collaboration among Florida International University (FIU), Miami Dade College (MDC), and Purdue University, the project established structured, reproducible educational and research pathways that recruit and advance students from institutions historically outside the fusion energy enterprise, building the human capital that this field urgently needs. The project integrates the complementary research strengths of FIU and Purdue to investigate flash sintering as a transformative processing route for tungsten-based PFCs. Unlike conventional sintering approaches, flash sintering offers rapid densification at significantly reduced thermal budgets, making it a compelling candidate for fabricating complex tungsten geometries that must withstand extreme plasma-facing environments. Systematic experimental and modeling efforts will elucidate the fundamental mechanisms governing microstructure evolution, grain boundary chemistry, and thermomechanical response during flash sintering — knowledge that is presently lacking but essential for translating this technology into reliable manufacturing practice. The convergence of workforce development and cutting-edge manufacturing research positions this project to deliver measurable, durable impact: a pipeline of fusion-ready researchers cultivated through expanded institutional partnerships, and a validated materials processing framework that accelerates domestic readiness for next-generation fusion reactor construction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is #BQP-complete in the worst case. In this work, we introduce QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

97 MATHEMATICS AND COMPUTING

Comparing Thermal Neutron Scintillators for Use With SiPM-Readout Detectors

Scintillator-based thermal neutron detectors for scientific scattering facilities offer an effective combination of large-area coverage and good spatial resolution. At Oak Ridge National Laboratory, silicon photomultiplier (SiPM)-readout Anger cameras using 6 Li glass scintillators have been developed, but the spatial resolution of these detectors is limited by the relatively low light yield of the glass. Recently, several brighter scintillator compositions with sufficient 6 Li concentration have emerged as promising candidates for higher-resolution imaging. Here, in this work, we evaluate five scintillator materials: GS20, LiF/ZnS:Ag, LiF/ZnO:Zn, LiI:Eu, and Cs 2 LiYCl 6 :Ce, each mounted on a SiPM Anger camera. For each scintillator, the neutron detection efficiency, spatial resolution, and count rate capabilities were measured and compared. Each of the new compositions achieved a spatial resolution better than 0.5 mm, compared to 0.66 mm for GS20, with LiI:Eu reaching the best value of 0.32 mm. Although these compositions improve the spatial resolution of the Anger camera, their longer pulse decay times limit their use in high count rate applications, and the camera’s hardware must be optimized for the different properties of the new scintillators.

Neutron detectors

Motor Configuration Selection for A New Technical Challenge to Develop A 5 MW Cryogenic Motor and Drive

Due to aviation’s appreciable and growing share of humanity’s impact on our environment and estimates that CO2emissions only account for 34% of aviation’s total effective radiative forcing [1], there is a need to reach beyond climate goals that focus only on CO2emissions, such as the US Aviation Climate Action Plan’s [3] goal to reach net-zero carbon emissions by 2050.There is motivation to develop technology that pushes toward future large transport aircraft with net zero climate impact that are highly electrified (i.e., have higher power electrical propulsion system components). This paper describes a new, 6-year technical challenge to address this need by developing a 5 MW superconducting motor and cryogenic drive. Section 1 will detail the motivation for this work. Section 2 will describe the technical challenge and the selected specifications for the motor. Section 3 will present the results of a motor configuration trade study and the down selection of one configuration to develop a detailed design for. The technical challenge focuses on the design of a5 MW superconducting motor and cryogenic drive and demonstration of it at a 2+ MW scale to achieve TRL 3. Both fully superconducting (superconducting stator and rotor) and fully cryogenic (superconducting rotor and cryogenic stator) machine configurations will be explored. An emphasis will be placed on addressing the key tall poles for high power superconducting machines. Further details will be included in the full paper. The requirements and goals of the motor will be detailed. The rated speed (2,000 to 3,000 rpm) is defined to be appropriate for directly driving multi-MW fans or propellers. A range of rated speed is permitted because the motor is not designed for a specific aircraft and to provide design flexibility if AC losses in the stator winding are found to be a significant constraint (i.e., a lower speed can be selected to reduce electrical frequency). Relatively conservative requirements for efficiency (99%) and specific power (20 kW/kg) are defined, because TRL advancement and pushing toward flight readiness is emphasized over performance optimization. However, more aggressive efficiency and specific power goals are specified (99.9% and 40 kW/kg). The 3rd section will present the results of a motor configuration trade study. The study started with a qualitative assessment of sixteen motor configurations based on geometric, mechanical, thermal, and electromagnetic criteria. This assessment has been completed with three evaluators scoring all nine criteria. A configuration down select was made by prioritizing the sixteen configurations into four tiers based on each configuration’s total score and consideration of manufacturability, complexity, and support hardware (e.g., rotary vacuum seals, bearings). Configurations in priority A and B will be further evaluated through quantitative assessments, whereas those in priority C will only be further evaluated if time permits and priority D will not be further evaluated. Eight of the sixteen configurations were down selected for quantitative assessment, which will include analytical calculations and low-to moderate-fidelity finite element analysis to produce a preliminary Pareto front of efficiency versus specific power for each configuration. This assessment emphasizes the calculation of AC losses in the stator winding and an exploration of thermal management approaches to remove that heat and maintain cryogenic temperature. The final paper will include a description of each motor configuration that was considered. The quantitative assessments are underway, and an assessment of one configuration is complete for multiple stator conductor options. The remaining assessments are scheduled to be completed by late March so that the final down select to one configuration can be included in this paper.

Net Zero

Robust Heat-Flux Sensors for Coal-Fired Boiler Extreme Environments

In this project, robust heat-flux measurement systems were developed. The heat-flux sensors utilize thermoelectric effects to directly transduce the heat-flux inputs to analog electrical voltage signals. They were constructed from dedicated materials that can withstand temperatures of at least 1000°C and maintain adequate performance at these conditions for prolonged periods of time. The proposed approaches took into account numerous considerations, including system cost, sensor head resilience, sensor footprint, data accuracy, response time, and maintenance requirements. Through modern thermoelectric materials design, methodical materials selection and rigorous testing in materials characterization labs and medium-scale fire research facilities, we have demonstrated functioning laboratory prototypes, upon which one could base industrial heat-flux sensing platforms capable of operating in the challenging high-temperature, corrosive environments of the boilers of coal-fired power plants. A distributed sensor array for heat-flux measurements throughout the furnace water-wall, the superheater area and the economizer coils can provide critical data for the power plant control systems to increase efficiency, improve safety and reduce down times. For example, the combined heat-flux sensor/control systems can contribute to the optimization of burner and boiler operations under flexible loads, the optimization of heat-exchange conditions and overall reduction of heat rate and emissions, the prediction of imminent overheating conditions, and the optimization of the soot-blowing protocols.

20 FOSSIL-FUELED POWER PLANTS

Synthesis and application of thermally responsive nanofiber coatings for overtemperature monitoring

This study presents a one-pot synthesis route to organometallic nanofibers based on copper thiolate, exhibiting distinctive chemical and physical characteristics. Electron microscopy analysis of morphology and composition revealed 2-10 μm-long, 50-90 nm-diameter hollow and non-hollow fibers composed of copper, sulfur, oxygen, hydrocarbon, and chlorine. Thermogravimetric analysis showed a pronounced mass loss within 120°C-135°C. To elucidate the thermal responsive pathways, the nanofibers were characterized before and after heating. X-ray photoelectron spectroscopy indicates that an initially mixed Cu(I)/Cu(II) oxidation states transition to predominantly Cu(I) upon heating. A layer of nanofiber was coated on battery pouch foil and evaluated as a candidate thermally sensitive coating. At elevated temperature (100-130°C), nanofiber coating released volatile organic compounds, sulfide and sulfur dioxide as detected using multiple gas sensors. This thermally responsive gas release/sensing approach provides a potential large-area temperature monitoring strategy, which is particularly relevant where direct temperature measurements of individual batteries is impractical. The results established proof of concept for nanofiber-coated battery pouch foil as overtemperature warning platform that can provide alerts when surface temperatures exceed a critical threshold. More broadly, the ability to form interconnected fiber networks positions copper thiolate nanofiber coatings as promising materials for advanced applications.

Ihala Gamaralalage, Chanaka [ORNL] (ORCID:00000002

Isotope engineering for spin defects in van der Waals materials

Abstract Spin defects in van der Waals materials offer a promising platform for advancing quantum technologies. Here, we propose and demonstrate a powerful technique based on isotope engineering of host materials to significantly enhance the coherence properties of embedded spin defects. Focusing on the recently-discovered negatively charged boron vacancy center ($${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$ V B − ) in hexagonal boron nitride (hBN), we grow isotopically purified h 10 B 15 N crystals. Compared to$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$ V B − in hBN with the natural distribution of isotopes, we observe substantially narrower and less crowded$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$ V B − spin transitions as well as extended coherence timeT 2 and relaxation timeT 1 . For quantum sensing,$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$ V B − centers in our h 10 B 15 N samples exhibit a factor of 4 (2) enhancement in DC (AC) magnetic field sensitivity. For additional quantum resources, the individual addressability of the$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$ V B − hyperfine levels enables the dynamical polarization and coherent control of the three nearest-neighbor 15 N nuclear spins. Our results demonstrate the power of isotope engineering for enhancing the properties of quantum spin defects in hBN, and can be readily extended to improving spin qubits in a broad family of van der Waals materials.

Science & Technology - Other Topics

Micrometer: Micromechanics transformer for predicting full field mechanical responses of heterogeneous materials

Predicting mechanical responses of heterogeneous materials across scales remains a significant challenge. Traditional computational methods often struggle with complex and multiscale nature of these materials, limiting their effectiveness in real-world applications. Here, in this paper, we introduce Micrometer, a vision transformer based deep learning model designed to predict full field mechanical responses of heterogeneous materials, bridging the gap between computer vision and solid mechanics problems. We show that Micrometer, trained on a large-scale high-resolution dataset of 2D fiber-reinforced composites, can achieve state-of-the-art performance in predicting microscale strain fields across a wide range of material properties and loading conditions. Our model demonstrates accuracy and computational efficiency in applications such as computational homogenization and multiscale modeling, reducing computational time by up to two orders of magnitude compared to conventional numerical solvers while maintaining less than 1 % errors in predicting macroscale stress fields. Furthermore, we showcase Micrometer’s adaptability through transfer learning experiments on new materials with limited data, highlighting its potential to tackle diverse scenarios in computational solid mechanics. These results represent a significant step towards AI-driven innovation in materials science, addressing the limitations of traditional numerical methods and paving the way for more efficient simulations of heterogeneous materials across various industrial applications.

Composite materials