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At least 55 records · Page 3

Simulation of Impedance Changes with Aging in Lithium Titanate-based Cells Using Physics-Based Dimensionless Modeling

Quantifying aging effects in lithium-ion cells with chemistries that have a flat open circuit potential is challenging. We implement a physics-based electrochemical model to track changes in the electrochemical impedance response of lithium titanate-based cells. Frequency domain equations of a pseudo two-dimensional model are made dimensionless, and the corresponding non-dimensional parameters are estimated using a Levenberg-Marquardt routine. The model weighs the relative contributions of changes in diffusion, ionic conduction within the electrolyte phase against solid phase electronic conduction towards cell aging. Solid-phase diffusion, charge transfer resistance and double layer capacitance at the solid-liquid interface are accounted for in the particle impedance. The estimation routine tracks dimensionless parameters using accelerated cycling data from full cells over 1000 cycles. The model can be deployed within a short time for state estimation using physics-based models without requiring prior knowledge of the battery chemistry, format, or capacity.

25 ENERGY STORAGE↗

Active and Stable PtPd Diesel Oxidation Catalysts under Industry‐Defined Test Protocols

Nanoparticle-supported Pt and Pd catalysts are employed industrially to convert CO and hydrocarbon residue from incomplete diesel fuel combustion into more environmentally-benign products. However, these catalysts deactivate over time due to sintering, especially for Pt nanoparticles which readily generate volatile species under high operating temperatures. Here, we turned the detrimental vapor-mediated sintering of Pt into an advantage by using a physical mixture of Pt and Pd catalysts prepared using a raspberry-colloid-templating (RCT) method. The RCT method produced Pt/Al 2 O 3 and Pd/Al 2 O 3 catalysts with partially embedded NPs to inhibit surface-mediated sintering pathways. As validated using an industry-defined emission control test protocol, aging a physical mixture of Pt/Al 2 O 3 and Pd/Al 2 O 3 at high temperature produced an alloyed PtPd/Al 2 O 3 catalyst that outperformed the fresh catalyst mixture and both individual catalysts for hydrocarbon conversion, while exhibiting high catalytic stability and resistance to sintering and to SO 2 poisoning. X-ray photoelectron spectroscopy revealed that in the aged catalyst mixture, half of the Pd content existed in the more active metallic state, compared to the less active oxide forms in the fresh mixture and both individual catalysts, explaining the unusual activity enhancement. Our results represent a practical approach to producing active and stable PtPd/Al 2 O 3 diesel oxidation catalysts for emission control applications.

Lim, Kang Rui Garrick [Harvard University, Cambrid↗

Poly(lactic acid)-Based Ink for Biodegradable Printed Electronics With Conductivity Enhanced through Solvent Aging

Biodegradable electronics is a rapidly growing field, and the development of controllably biodegradable, high-conductivity materials suitable for additive manufacturing under ambient conditions remains a challenge. Here, printable conductive pastes that employ poly(lactic acid) (PLA) as a binder and tungsten as a conductor are demonstrated. These composite conductors can provide enhanced stability in applications where moisture may be present, such as environmental monitoring or agriculture. Post-processing the printed traces using a solvent-aging technique increases their conductivity by up to 2 orders of magnitude, with final conductivities approaching 5000 S/m. Such techniques could prove useful when thermal processes including heating or laser sintering are limited by the temperature constraints of typical biodegradable substrates. Finally, both accelerated oxidative and hydrolytic degradation of the printed composite conductors are examined, and a fully biodegradable capacitive soil moisture sensor is fabricated and tested.

36 MATERIALS SCIENCE↗

Studies of LAPPD and HRPPD photodetectors for Cherenkov imaging applications

HRPPDs are the baseline single-photon sensors for a classic proximity-focusing RICH (pfRICH) counter, one of the Cherenkov radiation-based PID subsystems of the ePIC detector at the EIC. We report SPE time resolution of 87 ps rms for an LAPPD unit detecting Cherenkov photons in a quartz lens at a CERN PS test beam (2022). We also present the degradation and partial recovery of gain and relative efficiency of an LAPPD unit as a function of the B-field strength (up to 1.5 T) and angular orientation, measured with vertical dipole magnets at CERN (2023–2024). Finally, we report preliminary results of an accelerated ageing study performed on an HRPPD unit in Trieste laboratory (2025).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Aging phenomena in the two-dimensional complex Ginzburg-Landau equation

The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems which include coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability and spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations or oscillatory chemical reactions. Here, we employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate its non-equilibrium dynamics when the system is quenched into the “defocusing spiral quadrant”. We observe slow coarsening dynamics as oppositely charged topological defects annihilate each other, and characterize the ensuing aging scaling behavior. We conclude that the physical aging features in this system are governed by non-universal aging scaling exponents. We also investigate systems with control parameters residing in the “focusing quadrant”, and identify slow aging kinetics in that regime as well. Finally, we provide heuristic criteria for the existence of slow coarsening dynamics and physical aging behavior in the complex Ginzburg-Landau equation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A multilayer network analysis of Alzheimer's disease pathogenesis: Roles for p‐tau, synaptic peptides, and physical activity

INTRODUCTION: In the aging brain, cognitive abilities emerge from the coordination of complex pathways arising from a balance between protective lifestyle and environmental factors and accumulation of neuropathologies. METHODS: As part of the Rush Memory and Aging Project (n = 440), we measured accelerometer-based actigraphy, cognitive performance, and after brain autopsy, selected reaction monitoring mass spectrometry. Multilevel network analysis was used to examine the relationships among the molecular machinery of vesicular neurotransmission, Alzheimer's disease (AD) neuropathology, cognition, and late-life physical activity. RESULTS: Synaptic peptides involved in neuronal secretory function were the most influential contributors to the multilayer network, reflecting the complex interdependencies among AD pathology, synaptic processes, and late-life cognition. Older adults with lower physical activity evidenced stronger adverse relationships among phosphorylated tau peptides, markers of synaptic integrity, and tangle pathology. DISCUSSION: Network-based approaches simultaneously model interdependent biological processes and advance understanding of the role of physical activity in age-associated cognitive impairment. Highlights: Network-based approaches simultaneously model interdependent biological processes. Secretory synaptic peptides were influential contributors to the multilayer network. Older adults with lower physical activity had adverse relationships among pathology. There was interdependence among phosphorylated tau, synaptic integrity, and tangles. Network methods elucidate the role of physical activity in cognitive impairment.

60 APPLIED LIFE SCIENCES↗

A multi-physics constitutive model to predict hydrolytic aging in quasi-static behaviour of thin cross-linked polymers

The effect of hydrolytic aging on mechanical quasi-static responses of rubber-like materials, in particular, the idealized Mullins effect and permanent set have been modeled. The effect of hydrolytic damage on the mechanical integrity of the polymer matrix is modeled as the direct competition of two micro-structural phenomena (i) chain scission and (ii) reduction of cross-links. Both phenomena and their correlation were modeled and thus, the strain energy of the polymer matrix is written with respect to three independent mechanisms; i) the shrinking original matrix that has not been attacked by water, ii) conversion of the first network to a new network due to the reduction of the cross-links, and iii) energy loss from network degradation due to water attacks to polymer active agents. The proposed model satisfies the Clausius-Duhem inequality and is thus physically feasible. The model is validated with respect to sets of our experimental data and other sets available in the literature. The proposed model is based on the assumption of homogeneous diffusion and mainly relevant for thin samples. In view of its accuracy, interpret-ability, and deep insight it provides into the nature of damage accumulation, the model is a good choice for further implementation in FE applications.

42 ENGINEERING↗

Physics-Based Analysis of Cell Imbalances and Aging in Lithium-Ion Battery Modules and Packs

Lithium-ion battery (LIB) packs are a key solution for grid-scale energy storage, enabling grid resilience and supporting critical infrastructure. LIB modules and packs experience current imbalances and uneven cell aging due to various design and operational factors, and require a battery management system (BMS) to continuously monitor and control. In this context, a physics-based modeling framework for LIB modules and packs (liionpack) was enhanced to identify design and control strategies that minimize current imbalance and improve module/pack operation. Simulations of an 8-cell parallel-connected module demonstrate that reducing current imbalance leads to more uniform cell aging and improved module/pack-level degradation predictions. The analysis shows that current imbalance are affected by the electrical resistances. Terminal location significantly affects imbalance, with opposite-end terminal connections at intermediate branches minimizing the imbalance, and the pack circuit construction influences the accuracy of physics-based analysis at the pack scale. This framework enables design optimization of modules and packs through a fast and easy evaluation of pack performance and aging, and supports the development of aging-informed balancing strategies compatible with BMS implementation. Thereby, offering practical pathways to improve reliability and cycle life predictions in large-scale battery energy storage systems.

Ayalasomayajula, Surya Mitra [Oak Ridge National L↗

A physics-informed multi-agents model to predict thermo-oxidative/hydrolytic aging of elastomers

This paper introduces a novel physics-informed multi-agents constitutive model to propose prediction in quasi-static constitutive behavior of cross-linked elastomer and the loss of mechanical performance during environmental aging. The presented model is used to simulate the effect of single-mechanism chemical aging (i.e. thermal-inducedor hydrolytic aging) on the behavior of the material in this hybrid framework. Those environmental single-mechanism damages change the polymer matrix over time due to massive chain scission, chain formations, and changing the arrangement of molecules in the polymer matrix. Here we propose a data-driven super-constrained machine-learned engine to represent damage in the polymer matrix and capture the changes in material behavior, including its inelastic features such as Mullins effect and permanent set in the course of aging. We have simplified the 3D stress–strain tensor mapping problem into a small number of super-constrained 1D mapping problems by means of a sequential order reduction. An assembly of multiple replicated conditional neural-network learning-agents (L-agents) is trained to systematically simplify the high-dimensional mapping problem into multiple 1D problems, each represented by a different type of agent. Our hybrid framework is designed to capture the effect of deformation history, aging time, and aging temperature. The model is validated with respect to a comprehensive set of experiments specifically designed to benchmark model capabilities and also against available data in the literature. Thermodynamic consistency and frame independency have been verified. Besides acceptable predictive abilities, a significant reduction of computational cost to predict behavior at multiple states of deformation is the most significant feature of this model.

42 ENGINEERING↗

Study on the Thermal Stabilizing Process of Layered Double Hydroxides in PVC Resin

Poly(vinyl chloride) (PVC) is widely used in various fields and requires the use of thermal stabilizers to enhance its thermal stability during processing because of its poor thermal stability. Layered double hydroxides (LDHs) are widely considered to be one kind of highly efficient and environmentally friendly PVC thermal stabilizer. To investigate the thermal stabilizing process of layered double hydroxides (LDHs) in PVC resin, PVC and MgAl-LDHs powders with different interlayer anions (CO 3 2- , Cl - , and NO 3 - ) were physically mixed and aged at 180 °C. The structure of LDHs at different aging times was studied using XRD, SEM, and FT-IR. The results show that the thermal stabilizing process of LDHs on PVC mainly has three stages. In the first stage, the layers of LDHs undergo a reaction with HCl, which is released during the thermal decomposition of PVC. Subsequently, the ion exchange process occurs between Cl - and interlayer CO 3 2- , resulting in the formation of MgAl-Cl-LDHs. Finally, the layers of MgAl-Cl-LDHs react with HCl slowly. During the thermal stabilizing process of MgAl-Cl-LDHs, the peak intensity of XRD reduces slightly, and no new XRD peak emerges. It indicates that only the first step happens for MgAl-Cl-LDHs. The TG-DTA analysis of LDHs indicates that the interaction of LDHs with different interlayer anions has the following order: NO 3 - < CO 3 2- < Cl - , according to the early coloring in the thermal aging test of PVC composites. The results of the thermal aging tests suggest that LDHs with a weak interaction between interlayer anions and layers can enhance the early stability of PVC significantly. Furthermore, the thermal aging test demonstrates that LDHs with high HCl absorption capacities exhibit superior long-term stabilizing effects on PVC resin. This finding provides a valuable hint for designing an LDHs/PVC resin with a novel structure and excellent thermal stability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Changes in Distal Tibial Microarchitecture During Eight Weeks of U.S. Army Basic Combat Training Differ by Sex and Race

ABSTRACT Basic combat training (BCT) is a physically rigorous period at the beginning of a soldier's career that induces bone formation in the tibia. Race and sex are determinants of bone properties in young adults but their influences on changes in bone microarchitecture during BCT are unknown. The purpose of this work was to determine the influence of sex and race on changes in bone microarchitecture during BCT. Bone microarchitecture was assessed at the distal tibia via high‐resolution peripheral quantitative computed tomography at the beginning and end of 8 weeks of BCT in a multiracial cohort of trainees (552 female, 1053 male; mean ± standard deviation [SD] age = 20.7 ± 3.7 years) of which 25.4% self‐identified as black, 19.5% as race other than black or white (other races combined), and 55.1% as white. We used linear regression models to determine whether changes in bone microarchitecture due to BCT differed by race or sex, after adjusting for age, height, weight, physical activity, and tobacco use. We found that trabecular bone density (Tb.BMD), thickness (Tb.Th), and volume (Tb.BV/TV), as well as cortical BMD (Ct.BMD) and thickness (Ct.Th) increased following BCT in both sexes and across racial groups (+0.32% to +1.87%, all p < 0.01). Compared to males, females had greater increases in Tb.BMD (+1.87% versus +1.40%; p = 0.01) and Tb.Th (+0.87% versus +0.58%; p = 0.02), but smaller increases in Ct.BMD (+0.35% versus +0.61%; p < 0.01). Compared to black trainees, white trainees had greater increases in Tb.Th (+0.82% versus +0.61%; p = 0.03). Other races combined and white trainees had greater increases in Ct.BMD than black trainees (+0.56% and + 0.55% versus +0.32%; both p ≤ 0.01). Changes in distal tibial microarchitecture, consistent with adaptive bone formation, occur in trainees of all races and sexes, with modest differences by sex and race. Published 2023. This article is a U.S. Government work and is in the public domain in the USA. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Hughes, Julie M.↗

Simulated aging processes of black carbon and its impact during a severe winter haze event in the Beijing-Tianjin- Hebei region

Black carbon (BC) can mitigate or worsen air pollution through perturbing meteorological conditions. BC aging processes are important for the evolution of particle size, concentration, and optical properties of BC that determines its influence on the meteorology. Here we use the online coupled Weather Research and Forecasting-Chemistry (WRF-Chem) model to quantify the role of BC aging processes, including physical processes (PP) and absorption enhancements (AE), in exerting BC-induced meteorological changes and the associated feedback to PM2.5 (particulate matter less than 2.5 µm in diameter) and O3 concentrations during a severe haze event in Beijing-Tianjin-Hebei (BTH) region during 21-27 February 2014. Our results show that, compared to the simulation without the PP treatment, the simulated near-surface BC concentration and BC mass loading in BTH region is lowered by 6.6 % and 12.1 %, respectively, during the haze event with the PP included. PP increases the proportion of large-size BC (particle diameter greater than 0.312 µm) from 28 %-33 % to 59 %-64 % below 1000 m in BTH region. Both PP and AE enhance the “dome effect” of BC. With both PP and AE considered, a reduction in PBL height due to BC-PBL interaction is 116.3 m (20.7 %), compared to 75.7 m (13.5 %) without AE and 66.6 m (11.9 %) without both PP and AE. However, during this haze event, anomalous northeasterly winds are produced by the direct radiative effect of BC, which further affects the mixing and transport of aerosols. When PBL height is decreased (from 10:00 to 21:00), combining all the impacts on multiple meteorological factors, BC effect without PP and AE, without AE, and with PP and AE, respectively, increases surface concentrations of PM2.5 by 8.3 µg m-3 (6.1 % relative to the mean value), 6.1 µg m-3 (4.5 %) and 9.6 µg m-3 (7.0 %) but decreases surface O3 concentrations by 2.8 ppbv (7.4 %), 4.0 ppbv (9.0 %) and 5.0 ppbv (10.8 %) in BTH region averaged over 21-27 February 2014. Our results highlight the importance of the aging processes and absorption enhancements of BC in simulating weather and air quality.

Chen, Donglin↗

Modeling Chemo-Mechanics with Electrolyte Infiltration to Quantify Degradation of Cathode Particles

One of the main goals in modeling lithium-ion batteries is to improve/predict longevity and resilience of new chemistries. To that end, this talk investigates the formation of stress-induced fracture within polycrystalline cathode particles and the impact on capacity loss. Physically based cathode aging dynamics is simulated in a 3D, continuum-level chemo-mechanical model. The model captures anisotropic Li diffusion within a single polycrystalline particle comprised of hundreds to thousands of randomly oriented grains. A recent addition to this model includes electrolyte infiltration, which occurs when the electrolyte seeps into surface cracks within the particle. The model predicts that particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. Essentially, when neighboring grains are misaligned, they expand a different rates relative to one another leading to high stresses and ultimately the formation of intraparticle cracks. The model predicts that small particles with large grains develop significantly less damage than larger particles with small grains. Finally, the model predicts most of the chemo-mechanical damage accumulates in the first charge after formation. This chemo-mechanical "damage saturation" effect indicates that initial particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced. The principle contribution of this research is the use of an anisotropic chemo-mechanical model to test how particle geometry affect capacity fade, which predicts that particle size has a stronger effect on capacity fade than grain size and ultimately that small particles with large grains have the least capacity fade.

cathode↗

Component Assessment of the Electric Transmission Grid to Hurricanes

The increased frequency and intensity of extreme weather events from climate change necessitates understanding impacts on critical infrastructure, particularly electrical transmission grids. One of the foundational concepts of a grid's resilience is its robustness to extreme weather events, such as hurricanes. Resilience of the electric grid to high wind speeds is predicated upon the location and physical characteristics of the system components. Previous modeling assessments of electric grid failure were done at the systems level with assumptions on location and type of specific components. To facilitate more explicit adaptation metrics, accurate component-level information is needed. In this study, we build and utilize a data set of location, physical characteristics, and age of transmission structures for nine counties in the Florida Panhandle. These component characteristics were then simulated for failure under a variety of scenarios using fragility curves. Eight hurricanes were modeled using Hazus from the Federal Emergency Management Administration and the resulting impact to the network was assessed. The network was generated using the transmission lines and towers, showing increasing impacts to network efficiency with larger storms. Although modern transmission structures are built under the more stringent extreme wind loading construction standards, the prevalence of older, wooden transmission structures throughout the region poses a substantial risk to reliable electricity transmission during tropical cyclone events from the Gulf of Mexico.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Physiological Adaptations to Progressive Endurance Exercise Training in Adult and Aged Rats: Insights from the Molecular Transducers of Physical Activity Consortium (MoTrPAC)

While regular physical activity is a cornerstone of health, wellness, and vitality, the impact of endurance exercise training on molecular signaling within and across tissues remains to be delineated. The Molecular Transducers of Physical Activity Consortium (MoTrPAC) was established to characterize molecular networks underlying the adaptive response to exercise. Here, we describe the endurance exercise training studies undertaken by the Preclinical Animal Sites Studies component of MoTrPAC, in which we sought to develop and implement a standardized endurance exercise protocol in a large cohort of rats. To this end, Adult (6-mo) and Aged (18-mo) female (n = 151) and male (n = 143) Fischer 344 rats were subjected to progressive treadmill training (5 d/wk, ~70%–75% VO 2 max) for 1, 2, 4, or 8 wk; sedentary rats were studied as the control group. A total of 18 solid tissues, as well as blood, plasma, and feces, were collected to establish a publicly accessible biorepository and for extensive omics-based analyses by MoTrPAC. Treadmill training was highly effective, with robust improvements in skeletal muscle citrate synthase activity in as little as 1–2 wk and improvements in maximum run speed and maximal oxygen uptake by 4–8 wk. For body mass and composition, notable age- and sex-dependent responses were observed. This work in mature, treadmill-trained rats represents the most comprehensive and publicly accessible tissue biorepository, to date, and provides an unprecedented resource for studying temporal-, sex-, and age-specific responses to endurance exercise training in a preclinical rat model.

60 APPLIED LIFE SCIENCES↗

A mechanistic model for creep and thermal aging in Alloy 709

This report describes a physics-based model for creep and thermal aging in Alloy 709. Alloy 709 is an advanced austenitic alloy, targeted for use in future Sodium Fast Reactors (SFRs) and other advanced reactors. The material has superior high temperature properties compared to currently qualified 316 and 304 stainless steels. However, the available creep and thermal aging test database for Alloy 709 is significantly more limited compared to the historical materials. The physics-based model developed here is one way to accelerate the qualification of the material by providing more accurate long-term predictions for creep properties and thermal aging, compared to current empirical time-extrapolate techniques. The crystal plasticity finite element model is used to predict the deformation and failure of alloy 709. The same setup for the CPFE model is used in both the baseline model calibration process and the simulation campaigns for parameter inference. Specific constitutive choices are made for Alloy 709 to capture the primary deformation mechanisms. The dislocation creep formulation developed by Hu and Cocks is extended to account for coupled precipitation formation and the grain boundary cavitation model developed by Sham, Needleman, et al. is used to model grain boundary cavitation-induced failure. A novel update algorithm is proposed to render the semi-discrete constitutive update for the Sham-Needleman model unconditionally stable. A progressive calibration approach is adopted based on the observations that several types of material responses can be effectively decoupled. A surrogate model is trained based on full-fledged CPFE simulations to accelerate the forward model evaluations, and stochastic variational inference (SVI) is used to calibrate the unknown microstructural model parameters. The calibrated mechanistic model is used to predict the long-term creep life of Alloy 709, and the predictions are compared against classical empirical approaches.

36 MATERIALS SCIENCE↗

State-Specific Prevalence of Inactivity, Self-Rated Health Status, and Severe Joint Pain Among Adults With Arthritis — United States, 2019

Arthritis is associated with joint pain, disability, and physical inactivity, potentially resulting in poor quality of life. The Centers for Disease Control and Prevention analyzed 2019 Behavioral Risk Factor Surveillance System data to estimate state-specific arthritis prevalence and, among adults with arthritis, the prevalence of physical inactivity, fair/poor self-rated health status, and severe joint pain. Among adults with arthritis, age-standardized prevalences of physical inactivity, fair/poor health status, and severe joint pain were high in all states and highest in southeastern states. Increased promotion and use of evidence-based public health interventions for arthritis may improve health-promoting behaviors and health outcomes among adults with arthritis.

59 BASIC BIOLOGICAL SCIENCES↗

A Physically-Based Model for Thermo-Oxidative and Hydrolytic Aging of Elastomers

A computationally efficient model is proposed to capture the loss of mechanical performance due to chemical aging that are formed as the competition of chain scission and cross-link formation/dissolution, such as thermo-oxidative aging or hydrolytic aging. The model should be considered an extension of our recent models [1, 2, 3] which further simplifies the matrix behavior based on the assumption of independence of environmental and mechanical damage. The model uses this assumption to reduce the necessary material parameters needed to model constitutive and inelastic behavior of elastomers during aging. To this end, the model can provide accurate predictions of the material performance with the significantly fewer number of fitting parameters. The model is relevant for all decay mechanisms formed by the occurrence of two simultaneous micro-mechanisms; (i) formation/reduction of the cross-links, and (ii) chain scission, both of which are present in thermo-oxidation and hydrolytic aging. Assuming the alteration of the chain density along the aging trajectory is identical to the peroxide cross-link density for thermo-oxidation, and the change of the average molecular weight for hydrolysis, the strain energy of polymer matrix can be rewritten as a function of deformation, deformation history, storage time and aging temperature. Next, the modified network alteration model is formulated for implementation into Finite Element (FE) simulations. The model is built on the presumption of homogeneous and consistent oxygen/water absorption and thus is mainly relevant for relatively thin samples exposed to environmental loads for a long time. The proposed model includes only six physically inspired material parameters. Therefore, while it is computationally efficient, it shows good agreement with own experimental data, which performed on various range of accelerated aging temperatures and times. With respect to its computational efficiency, simplicity, accuracy, and interpret-ability, the model is the right choice for advanced implementations in FE programs.

42 ENGINEERING↗