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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Fuel performance analysis of fully-resolved TRISO compact

The TRi-structural ISOtropic (TRISO) fuel multilayered coating structure offers multiple barriers to fission product release, enhancing safety and performance. The heterogeneous nature of TRISO fuel compacts, comprising thousands of randomly distributed coated fuel particles embedded in a graphite matrix, creates intricate stress fields and thermal gradients that cannot be accurately modeled using simplified one-dimensional or homogenized approaches. Consequently, three-dimensional modeling enables the prediction of fuel compact dimensional changes, internal pressure buildup, and fission product transport pathways under diverse irradiation and thermal conditions. This capability facilitates detailed analysis of particle-to-particle interactions, matrix cracking mechanisms, and the statistical distribution of coating failures, which directly impact fuel performance and safety margins. This capability is particularly critical for advanced reactors, such as high-temperature gas-cooled reactors and other Generation IV reactor designs where TRISO fuel operates at elevated temperatures and burn-up levels. This work introduces a novel method to generate an optimized packing of TRISO compacts and a complete 3D mesh with random distribution of TRISO particles, which are discretized into each coating component layer.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Evidence Theory Representations for Properties Associated With Weak Link/Strong Link Systems, Part 3: Margins for Failure Time and Failure Temperature

The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of time and temperature margins associated with loss of assured safety (LOAS) for one weak link (WL)/two strong link (SL) systems is illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) SL/WL failure time margins defined by (time at which SL failure potentially causes LOAS) – (time at which WL failure potentially prevents LOAS), (ii) SL/WL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) – (the temperature at which WL failure potentially prevents LOAS), and (iii) SL/SL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) – (the temperature of SL whose failure potentially causes LOAS at the time at which WL failure potentially prevents LOAS).

42 ENGINEERING↗
DOE OSTI2021

Characterization of damage processes in Montney siltstone under triaxial compression using acoustic emission and diagnostic imaging

SUMMARY Crack nucleation and rock failure processes in a fine-grained siltstone (Montney Formation) under triaxial compression are investigated using combined diagnostic techniques, including ultrasonic-wave measurement, acoustic-emission (AE) monitoring, computed tomography (CT) scanning, and thin-section imaging. The sample displays a weak-to-moderate inherent seismic anisotropy and noticeable stress-induced anisotropy prior to failure. No AE event was detected until the applied axial stress reached 95 per cent of the peak value. The signal-to-noise ratio is relatively low, however, and detectable AE events are more diffuse than those observed in highly brittle rocks. The AE locations correlate with a shear fracture zone imaged by CT scanning. AE moment-tensor analysis reveals that events with larger relative magnitudes are characterized by high volumetric (tensile or compressive) components, and the initiation of the failure zone is dominated by combined shear-tensile (ST) failure. Stress inversion of the AE events with high tensile components is in good agreement with the known applied stress. Microscopic imaging of thin sections from the failed sample shows that the failure zone is an en echelon structure consisting of a major fracture with branching micro and minor cracks. This failure mechanism is consistent with a ST source mechanism and is interpreted to be associated with the fine granular structure and mineral composition of Montney siltstone.

Jia, Suzie Q. (ORCID:0000000326496190)↗
DOE OSTI2024

Estimating the Contributions to Human Error Probability from the Convolution of the Distribution of Time Available and Time Required

As part of their duties, Human Reliability Analysis must often evaluate if crews in nuclear power plants (NPPs) can complete tasks associated with a human-failure event within time limits. For example, the time required in NPP scenarios is determined by systematic and structured walkthroughs, feasibility studies, recorded times from training exercises, and interviews with experienced operators and experts. Typically, a point estimate is derived for the estimate (mean, maximum, or 95th percentile of time required). Using point-estimate values can mask the risk associated with variability among crews, plant conditions and set-up, environmental conditions, and other impact factors under which these actions are executed. While point estimates for time required and time available have served the industry well, without considering the uncertainty they could lead to biased understanding about the risk. The Integrated Human Event Analysis System - General Methodology (IDHEAS-G) model (developed by the US Nuclear Regulatory Commission, NRC) for human error probability calculates human error probability by summing two probabilities: insufficient time and cognitive error. As such, the model takes a more holistic approach by considering the full distributions for time required and time available to calculate the human error probability because the time available to complete the task is insufficient. In this study, we expand on the work of the NRC and discuss methods for estimating these time considerations. For example, for the time required, the impact of Performance Influencing Factors (PIFs) on the distribution was divided into impacts that are aleatory in nature, such as crew-to-crew variability, and those that are epistemic (i.e., the PIFs). Starting with the factors that introduce aleatory uncertainty, a first-order distribution was developed from a large set of time required (i.e., NPP task completion times) data for the range of operator actions that occur in the NPP control room under simulated accident conditions. The first-order distribution can then be adjusted to account for epistemic uncertainty using research associated with the impact of applicable PIFs on the time required. We also develop guidance for analysts to address the probability distributions for the time available. The guidance we developed on how to estimate time required and time available distributions is based on the identification of pertinent research and data, data analyses, and expert knowledge elicitation.

human error probability, human performance, time e↗
DOE OSTI2024

Implications of pond reliability on the techno-economic and life cycle environmental impacts of algal biofuels

Despite extensive research on algal bioproducts, there is limited understanding of how pond contamination affects their economics and environmental impacts. This work compared the costs and environmental impacts of algal biofuels across different pond failure scenarios. Pond failure was simulated by a reliability model based on pond mean-time-to-failure (MTTF). The reliability model was integrated with a process model to analyze the impacts of pond failure on the operations of algal farms and biorefineries. Process model outputs were used for techno-economic analysis and life cycle assessment to determine the minimum fuel selling price (MFSP), global warming potential (GWP), and freshwater consumption impacts of algal biofuels for five MTTF scenarios of 20, 54, 80,120, and 350 days, assuming an average mean-time-to-reset of 7 days. Results show that higher MTTFs reduce the cost and environmental impact of algal biofuels, but with diminishing returns. The average MFSPs for the 20-day, 54-day, and 350-day MTTF scenarios were $\$3.52$, $\$2.54$, and $\$2.10$ per liter of gasoline equivalent, respectively. The GWP for the same scenarios were 131, 96, and 83 g CO 2eq MJ –1 , respectively. This study highlights the significant impact of larger seed trains, required under low MTTFs, on the costs and greenhouse gas emissions of algal biofuels. Moreover, the work shows that algal biofuels fail to be cost-competitive with conventional fuels, even when productivities are increased from 17 to 35 g m –2 d –1 . Furthermore, this work is the first to explore the implications of pond failure on the sustainability of algal biofuels and provides valuable insights to algae farmers on how to reduce the costs and financial risks of algal cultivation through process design and pond management strategies.

09 BIOMASS FUELS↗
DOE OSTI2024

ASME – Grappling with the Concept of Component Failure

ASME concepts of component failure. Definition for failure, functionality, damage tolerance, including Magnox reactors and AGRs. How ASME is addressing damage tolerance, and Section III division 5 Design, Classification, Reliability Target for SRC-1 components, Basic analysis approach, simple assessment, and full assessments, Reference to reliability and integrity management and strategy for graphite components.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Failure Strain and Related Triaxiality of Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 Metals, Part I: Experimental Investigation

The objective of this study is to develop failure-limit material models for Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 metals, based on parameters of plastic equivalent strain (failure strain) and stress triaxiality. The research is conducted in two parts. This paper presents Part One of the study. In Part One, custom-designed test specimens undergo controlled uniaxial tension and compression testing at ambient temperature. These tests are performed at quasi-static speeds using Universal Testing Machines (UTMs) in accordance with ASTM E8 and ASTM E9 standards. Experimental data, specifically engineering stress–strain and force–displacement curves, are recorded from the onset of loading until specimen fracture, or in the case of compression tests, until the capacity of the testing machine is reached. In Part Two, the emphasis shifts to the calibration of Finite Element Analysis (FEA) models of the custom-designed test specimens. Plastic equivalent strain and the corresponding stress triaxiality values at failure are extracted from each test specimen for the given metal. These values are then systematically plotted onto a single graph to construct the failure-limit curve, which delineates the boundary conditions for material failure. This approach will facilitate the development of a comprehensive material property definition that correlates plastic equivalent strain with stress triaxiality at failure for Aluminum 6061-T6, A36 Carbon Steel, 304 Stainless Steel, and Nitronic 60 metals.

Harwell, Ron↗
DOE OSTI2020

Concentration dependent properties and plastic deformation facilitate instability of the solid-electrolyte interphase in Li-ion batteries

Lithium-ion batteries (LIBs) often suffer from capacity fading and poor cyclic performance due to mechanical degradation of the solid-electrolyte interphase (SEI). Here we perform numerical simulations and theoretical analysis to elucidate the role of plasticity in wrinkling and ratcheting behaviors of an SEI/electrode system. A coupled diffusion and finite deformation framework is formulated and numerically implemented as a user-element subroutine (UEL) to describe transient lithium diffusion and accompanying elastic–viscoplastic deformation of the electrode. It is found that concentration dependent properties and plastic deformation facilitate wrinkling in such a system. A wrinkled morphology may further lead to ratcheting and related failure under cycling. A phase diagram of four types of cyclic behaviorsis identified in terms of the charging rate and time. Our analysis suggests several potential strategies to avoid wrinkling and ratcheting instabilities, such as charging/discharging the electrode at a sufficiently slow rate, and/or introducing a thick artificial SEI with a pre-tension.

25 ENERGY STORAGE↗
DOE OSTI2022

Designing Cladded Components for High Temperature Nuclear Service: Part I—Analysis Methods

Use of corrosion-resistant cladding can greatly extend the design life of structural components in many advanced reactor systems. However, there are currently no ASME design rules for cladded components to guard against creep-fatigue failure and ratcheting strain accumulation in elevated temperature nuclear service. This paper, presented in two parts, addresses this gap by proposing a design strategy for cladded components that do not require long-term testing of clad materials. The proposed approach relies on approximate design analysis methods for two types of clad materials—a soft clad that creeps much faster than and has lower yield stress than the class A base material and a hard clad that creeps much slower than and has higher yield stress than the class A base material. Part I discusses the approximate analysis strategies for the clad materials—treat a soft clad as perfectly compliant and a hard clad as linear elastic—and Part II develops a complete set of design rules for each of the two types of cladded components. In conclusion, finite element analyses of representative high temperature reactor components show that the proposed design analysis methods can bound the design quantities in soft cladded components and approximate the design quantities in hard cladded components.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Transformational faulting in Mn 2 GeO 4 from olivine to wadsleyite structure: Implications for physical mechanism of deep-focus earthquakes

High-pressure and temperature deformation experiments interfaced with acoustic emission (AE) monitoring have been conducted to study transformational faulting in Mn 2 GeO 4 olivine, which transforms to the β phase, isostructural to wadsleyite. Metastable Mn 2 GeO 4 olivine exhibits a marked embrittlement behavior at temperatures between 800 and 1100 K, emitting numerous AEs. At each temperature, brittle deformation is characterized by a two-stage process: (1) a “preparation” stage with numerous diffusedly located low-magnitude AEs and large b values (>2), and (2) a failure stage where larger-magnitude AEs form a planar distribution with b values about 1. Microstructure analysis reveals extensive kink band development in olivine grains in the recovered samples. Kink band boundaries (KBBs), with a typical thickness of ∼100 nm, are filled with a nanometric β-Mn 2 GeO 4 “gouge”. A dense array of secondary shear localizations is often present within the kink bands, suggesting significant shear deformation therein. The combined observations suggest that faulting in metastable Mn 2 GeO 4 olivine is a self-similar process, from grain-scale to the sample-scale. Both observed embrittlement behavior and the microstructure of metastable Mn 2 GeO 4 olivine are essentially identical to those in Mg 2 GeO 4 olivine we have reported previously, indicating that the physical mechanism of faulting in metastable olivine is insensitive to the specific crystallographic structure of the high-pressure phase. The low b values (about 1) observed in the faulting process in our experiments are similar to those of deep focus earthquakes in cold subduction zones. Our observed mechanism explains deep focus seismicity in cold metastable mantle wedges, provided that the self-similarity assumption holds to geological scales.

58 GEOSCIENCES↗
DOE OSTI2022

Intermediate polaronic charge transport in organic crystals from a many-body first-principles approach

Abstract Charge transport in organic molecular crystals (OMCs) is conventionally categorized into two limiting regimes − band transport, characterized by weak electron-phonon (e-ph) interactions, and charge hopping due to localized polarons formed by strong e-ph interactions. However, between these two limiting cases there is a less well understood intermediate regime where polarons are present but transport does not occur via hopping. Here we show a many-body first-principles approach that can accurately predict the carrier mobility in this intermediate regime and shed light on its microscopic origin. Our approach combines a finite-temperature cumulant method to describe strong e-ph interactions with Green-Kubo transport calculations. We apply this parameter-free framework to naphthalene crystal, demonstrating electron mobility predictions within a factor of 1.5−2 of experiment between 100 and 300 K. Our analysis reveals the formation of a broad polaron satellite peak in the electron spectral function and the failure of the Boltzmann equation in the intermediate regime.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Confidentiality-preserving machine learning algorithms for soft-failure detection in optical communication networks

Automated fault management is at the forefront of next-generation optical communication networks. The increase in complexity of modern networks has triggered the need for programmable and software-driven architectures to support the operation of agile and self-managed systems. In these scenarios, the European Telecommunications Standards Institute zero-touch network and service management approach is imperative. The need for machine learning algorithms to process the large volume of telemetry data brings safety concerns as distributed cloud-computing solutions become the preferred approach for deploying reliable communication network automation. This paper’s contribution is twofold. First, we propose a simple yet effective method to guarantee the confidentiality of the telemetry data based on feature scrambling. The method allows the operation of third-party computational services without direct access to the full content of the collected data. Additionally, the effectiveness of four unsupervised machine learning algorithms for soft-failure detection is evaluated when applied to the scrambled telemetry data. The methods are based on factor analysis, principal component analysis, nonlinear principal component analysis, and singular value decomposition. Most dimensionality reduction algorithms have the common property that they can maintain similar levels of fault classification performance while hiding the data structure from unauthorized access. Evaluations of the proposed algorithms demonstrate this capability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Assessment and validation of NEAMS tools for high-fidelity multiphysics transient modeling of microreactors: Application of NEAMS codes to perform multiphysics modeling analyses of micro-reactor concepts

The NEAMS Multiphysics Applications team aims at providing assessment of code useability and functionality for microreactor design and analyses, together with demonstration of their capabilities to properly capture the steady-state and time-dependent behavior of different microreactor concepts. In FY-24, significant progress was achieved in improving multi-physics models of several microreactors systems: HP-MR, GC-MR and KRUSTY. These efforts focused on solving more complex multiphysics problems enabled by enhanced tools capability, verifying and validating results obtained, providing feedback to developers for suggested improvements, and sharing these models to facilitate user training. A series of new multiphysics transients were completed on the HP-MR (using Griffin/BISON/Sockeye) with core startup transient, control drum inadvertent rotation accident, and hydrogen leakage from hydride moderator (also including SWIFT). On the GC-MR, a new full-core model was developed and analyzed through a series of new multiphysics (Griffin/BISON/SAM) transients to simulate moderator leakage (also including SWIFT), flow blockage and coolant depressurization. Additional and updated TRISO failure analyses were completed on the HP-MR unit-cell and GC-MR assembly models leveraging improved TRISO modeling capabilities. The amount of SiC failure following accidental transients at end-of-life was null. However, GC-MR assembly TRISO analysis highlighted Pd penetration rate can be problematic and may require design changes on the studied microreactor concept. The neutronics discrepancies observed on the KRUSTY model in previous years were resolved using hybrid set of Monte Carlo/Deterministic cross-sections. The multiphysics (Griffin neutronics / BISON thermal-mechanics) 15₵ insertion transient simulation displayed good agreement when comparing with experimental data. Initial modeling of the 30 ₵ reactivity insertion also displays promising results. Such close agreement provides important validation data that can be leveraged by the NEAMS program and by microreactor vendors to support licensing of their technology. Finally, important experience was gathered with the NEAMS tools leading to several user feedback shared with tools developers, especially with regards to MOOSE mesh generator and Griffin. This project led to many publications demonstrating modeling capabilities, and to three models shared on the Virtual Test Bed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

INL Background, Capabilities, and Research Discussion for Potential COG Collaborations

Slides discussing general INL capabilities in a variety of research areas including LWRS, Plant Modernization, Risk-Informed Systems Analysis, the INL Digital Innovation Center of Excellence DICE, integrated online dynamic plant models, online deterministic failure-mode and reliability models of plant systems, equipment and components, and plant information models.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2026

3D TRISO particle-explicit compact meshing

The TRI-structural ISOtropic (TRISO) layered fuel particle is a robust nuclear fuel form offering enhanced safety and performance for advanced reactor concepts, including high-temperature gas-cooled reactors and other Generation IV designs. These poppy-seed-sized particles are embedded in a graphite matrix to form fuel elements that must withstand elevated temperatures and high burn-up levels. The heterogeneous nature of these fuel elements — comprising thousands of randomly distributed TRISO particles — produces complex stress fields and thermal gradients that one- and two-dimensional models cannot accurately capture. While three-dimensional modeling has improved predictions of dimensional changes, internal pressure buildup, and fission product transport under irradiation, current approaches rely on homogenized material properties that are known to have considerable divergence from experimental observations. This work presents a methodology for optimized random packing of TRISO fuel compacts and full three-dimensional mesh generation within the BISON fuel performance code, with each particle coating layer individually discretized. The resulting mesh was demonstrated through heat conduction simulations under representative in-reactor operating conditions, showing strong agreement with expected behavior. This capability enables detailed analysis of particle-to-particle interactions, matrix cracking mechanisms, and the statistical distribution of coating layer failures — all of which directly govern fuel performance and safety margins.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Validation of MFUEL Metal Fuel Performance Models of SAS4A/SASSYS-1

The fuel characterization models of SAS4A/SASSYS-1 (SAS) have recently been extended to include a new U-Pu-Zr metal fuel model, MFUEL. MFUEL is equipped with mechanistic physics based models to predict the pre-transient characterization and transient response of metal fuel, with emphasis on fuel melting, cladding failure, and the metal fuel’s impact on core reactivity. The MFUEL model will be available in the full version of SAS4A/SASSYS-1 5.7, which is scheduled to be released in June 2023. Fast reactor fuel pins that operated in EBR-II and FFTF with low smear density U-Zr and U-Pu-Zr metal fuels and irradiation resistant ferritic-martensitic cladding showed significant advantages in achieving high burnups and assuring inherent safety characteristics during anticipated transients, design basis events, and beyond design basis events. For safety analysis, a fuel performance model must be able to predict (1) Fuel pin mechanics and compositional and dimensional changes, (2) Clad failure, and (3) Fuel pin thermal resistance. Achieving these high level goals accurately is strongly related to the model performance of individual physical processes taking place within a fuel pin during its lifetime. Metal fuels typically operate above the mid-point temperature of melting during normal, as well as off-normal, conditions. At these elevated temperatures, the availability of thermal activation provides a driving force for various diffusional processes leading to complex phase transformations, micro-structure evolution, significant amounts of fuel swelling, interconnected porosity formation, excessive amounts of fission gas release, and fuel clad chemical interactions. Clad failure in fast reactors primarily occurs as a result of creep rupture augmented by clad wastage formation. The reaction is driven by thermal creep induced dislocation motion, grain boundary cavity nucleation, growth and breakup of grain boundaries. The high level complexity and limited available data requires introducing physics-based modeling approaches to gain extrapolation ability and sensitivity with respect to various conditions. The objective of this report is to perform validation of MFUEL using the experimental data for (1) Normal operation EBR-II fuel behavior, (2) Normal operation PHENIX fuel behavior, (3) HT9 Pressure tube ramp-and-hold creep rupture tests, (4) Whole Pin Furnace (WPF) creep strain, creep rupture and eutectic tests, (5) Fuel Behavior Test Apparatus (FBTA) eutectic tests, and (6) TREAT M5-7 OverPower tests up to clad failure. Section-2 includes a brief description of the MFUEL models. A detailed description of the MFUEL physics-based, semi-empirical models will be presented in the SAS V 5.7 theory manual. Section-3, 4, and 5 describes the validation effort for the pre-transient irradiation, furnace transients, and TREAT M-Series transients, respectively.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Surrogate-assisted optimization under uncertainty for design for remanufacturing considering material price volatility

Remanufacturing is a well-established end-of-life (EOL) strategy that promises significant savings in energy and carbon emissions. However, the current design practices are not remanufacturing-inclusive, i.e., the majority of products are designed for a single life cycle. As a result, potential products that can sustain multiple life cycles are deprived of additional benefits of being designed for remanufacturing, such as reduced material usage, lower cost, and improved environmental impact. Moreover, the uncertainty in design, material selection, and economics are not considered to produce remanufacturable designs. Accordingly, this research proposes a design for remanufacturing (DfRem) framework that accounts for design uncertainty and material price volatility. The framework systematically explores the design space, performs design optimization under uncertainty, followed by topology optimization to provide additional mass savings, and finally, a price volatility analysis for plausible design material choices. The candidate designs are evaluated based on their design mass, material price volatility, failure mode characteristics, carbon footprint, and embodied energy impacts. The proposed framework's utility is demonstrated via the use of an engine cylinder head case study subjected to thermo-mechanical loads along with fatigue and wear failure. Considering grey cast iron and aluminum alloy as the design material choices, it was found that the cast iron design reduced the initial design mass by 6% as opposed to a 5% decrease for aluminum. On the other hand, about 8% area of the cast iron design failed due to fatigue, compared to 3% for aluminum. Here, we further observed that although the aluminum design provided better mechanical performance than the cast iron design, this material was more expensive and volatile in price.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Insights Into Thermal Runaway Mechanisms: Fast Tomography Analysis of Metal Agglomerates in Lithium-Ion Batteries

Thermal Runaway (TR) in lithium-ion batteries (LIB) is a critical technological and social concern. Whilst such events are rare, TR is characterized by uncontrollable heating leading to catastrophic failures. To deepen the understanding of the failure process and subsequently develop more accurate TR prediction models and as a result safer battery systems, we present in this work high-speed X-ray tomography for in-depth investigations of the copper current collector melting and agglomeration during TR. The melting process presents valuable real-time internal information about heat evolution during TR, previously challenging to access but crucially important for validating TR models. In this work, controlled failure studies combined with high-speed X-ray tomography were performed on two different commercial LIB models, subjecting them to both external heating and nail penetration to induce TR. Through real-time observation via high-speed tomography, followed by segmentation, rendering, and analysis, the formation of copper agglomerates was qualitatively and quantitatively characterized and visualized for the first time. Agglomerates tended to form either from the battery's outermost layers or centrally, depending on the method of TR initiation, and gives an indirect insight into the internal temperature evolution and distribution. Moreover, an initial comparative analysis between the battery models also revealed differences in agglomerate size, which has been linked to the thicker copper current collectors of one of the cell models. We further discuss the impact of larger copper agglomerates on heat distribution and safety. This study not only sheds light on the intricate dynamics of TR in LIBs but also underscores the pivotal role of 'gold-standard' imaging techniques in advancing battery safety, crucial for the robust modeling of TR and the future design of electric vehicle safety systems.

25 ENERGY STORAGE↗