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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Effects of midplane density gradient in the propagation of high-harmonic fast waves considering high temperature anisotropy in the scrape-off layer of NSTX-U

High-Harmonic Fast Wave (HHFW) heating experiments in NSTX have shown that up to 60% of the injected power can be lost in the Scrape-Off Layer (SOL) when the density is above the fast wave cutoff density in front of the antenna, for which the fast wave is able to propagate into the plasma. This work models HHFW propagation in the SOL plasmas of NSTX-U using a 2D divertor SOL profile derived from the pressure assumption and the finite element temperature solution, which accounts for the high anisotropy of heat conduction in a 2D axisymmetric geometry. In this work, the two-dimensional axisymmetric SOL temperature profile is first evaluated by solving the steady-state non-linear heat conduction equation, in which thermal conductivity depends on temperature, using a finite element approach in the Petra-M workbench. A 2D density profile is then obtained from a prescribed density profile at the outer midplane assuming pressure is uniform along a flux tube in the SOL. This approach results in density and temperature profiles in which the strong asymmetric nature of heat conduction between the parallel and perpendicular background magnetic field is successfully captured. Furthermore, this work focuses on investigating the effect of the SOL plasma density profile on parasitic HHFW propagation in the SOL. The simulation results show that the radial gradient of the density profile affects the wavefield propagation in the SOL. As the density profile broadens, the wavefield intensity and its poloidal extent are reduced in the SOL, and the core coupling increases. Similarly, as shown by collisional power deposition, a proxy for power absorption, the fraction of power deposited in the SOL decreases with a broadening profile.

HHFW↗
DOE OSTI2024

Accelerating Thermochemical Equilibrium Calculations for Nuclear Reactor Applications

Thermochemical properties play a key role in modeling and simulation of several key phenomena in nuclear reactors. There has been an increasing interest in incorporating CALPHAD-based formulations in multiphysics simulations including for Molten Salt Reactors where knowledge of phase evolution of the salt and the chemical potentials of various elements are of utmost importance in source term analyses and redox control. However, the size of such simulations is often limited by the high computational cost of full thermodynamic equilibrium calculations. This work discusses the current efforts aimed at accelerating thermochemical equilibrium calculations for multiphysics simulations performed using the open-source finite element / finite volume code Multiphysics Object Oriented Simulation Environment (MOOSE) [1]. While several methods have been proposed for accelerating phase equilibrium calculations [2], most focus on relatively small systems and often rely on a- priori knowledge of the state-space of the system. Nuclear materials, however, are often multi-component systems owing to the evolution of composition under irradiation and an approach based on a-priori mapping of phase diagram is often not enough. This work is aimed at demonstrating an on-the-fly surrogate modeling framework that uses active learning to reduce the number of full equilibrium calculations that must be performed. By combining with efficient coupling approaches, the surrogate framework helps in reducing the computational cost of thermodynamic equilibrium informed multiphysics simulations of nuclear materials. The performance is benchmarked against full coupling with the thermochemistry library Thermochimica [3]. This work uses a machine learning based approach for constructing surrogate models to predict the stable phases in a multicomponent system. The surrogates were constructed using neural networks and Gaussian process classification. In this work, we compare the relative performance of the two methods. We also demonstrate the use of caching previous calculations by interpolating the values from nearest neighbors. References [1] Lindsay, A.D., et al. "2.0 – MOOSE: Enabling massively parallel multiphysics simulation", SoftwareX, 20 (2022): 101202. [2] Roos, W.A. and Zietsman J.H. "Accelerating complex chemical equilibrium calculations – A Review", Calphad, 77 (2022): 102380. [3] Piro, M.H.A., et al. "The thermochemistry library Thermochimica", Computational Materials Science, 67 (2013): 266-272.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Brittle failure analysis and modeling of high-burnup PWR fuel cladding alloys

The aim of this research is the development of methods for predicting mechanical behavior and identification of limiting conditions to prevent brittle failure of high-burnup (HBU) pressure water reactor (PWR) fuel cladding alloys. A finite element (FE) model of the ring compression test (RCT) was created to analyze the failure behavior of zirconium-based alloys with radial hydrides during the RCT. An elastic-plastic material model describes the zirconium alloy. The stress-strain curve needed for the elastic-plastic material model was derived by inverse finite element analyses. Cohesive zone modeling is used to reproduce sudden load drops during RCT loading. Based on the failure mechanism in non-irradiated ZIRLO (R) claddings, a micro-mechanical model was developed that distinguishes between brittle failure along hydrides and ductile failure of the zirconium matrix. Two different cohesive laws representing these types of failure are present in the same cohesive interface. The key differences between these constitutive laws are the cohesive strength, the stress at which damage initiates, and the cohesive energy, which is the damage energy dissipated by the cohesive zone. Statistically generated matrix-hydride distributions were mapped onto the cohesive elements and simulations with focus on the first load drop were performed. Computational results are in good agreement with the RCT results conducted on high-burnup M5 (R) samples. It could be shown that crack initiation and propagation strongly depend on the specific configuration of hydrides and matrix material in the fracture area.

Simbruner, Kai↗
DOE OSTI2025

A Domain-Decomposed A-ϕ Formulation Based on Lagrange Multipliers for Low-Frequency Problems

A domain-decomposed A-ϕ formulation based on Lagrange multipliers is proposed to simulate low-frequency elec- tromagnetic problems. This method partitions the computational domain into smaller subdomains, allowing each subdomain to be independently formulated using Lagrange multipliers as Dirichlet boundary conditions, while ensuring continuity of the fields across the interfaces. A mixed finite element method, utilizing both vector and scalar basis functions, is employed to discretize the formulation, resulting in a global system to be solved. The proposed method is validated using TEAM Problem 7 at 50 Hz, demonstrating its effectiveness in handling complex geometries and addressing the low-frequency breakdown issues commonly encountered in traditional finite element methods.

Hossain, Amzad↗
DOE OSTI2025

Radiation-induced bowing of SiC/SiC composites under neutron flux gradients—integral experimental data for model validation

Here, the radiation-induced swelling of SiC and its composites, including strong dependencies on temperature and dose, can drive significant lateral bowing in the presence of temperature and/or dose gradients. In recent years, simulations have been performed to assess the extent of bowing in SiC composite light-water reactor (LWR) fuel cladding and boiling water reactor (BWR) channel boxes. However, to date, no integral experimental data exist to validate these models. This work provides the first experimental bowing evaluation of three ∼380 mm long SiC composite specimens irradiated under varying neutron dose gradients (∼50°C–60°C, 0.03–0.06 dpa): two tubes (∼9.8 mm diameter) and a miniature BWR channel box (∼30 mm square). The measured radiation-induced length swelling (∼0.3%–0.7% linear) was consistently 10%–21% higher than values obtained from 3D finite element structural analyses with inputs from 3D radiation transport calculations. This discrepancy could be at least partially explained by differences in dose rate (∼10 -8 dpa/s) compared to the literature data (∼10-6 dpa/s) used to establish the dose-to-swelling correlations in the model. Nevertheless, the modeled bowing magnitudes (<2 mm) obtained from finite element analyses and simple analytical equations were within the bounds of the experimental measurements for all specimens. With improved confidence in the ability to predict the structural response and measure the macroscopic deformations, future experiments will target transient bowing under neutron flux gradients at representative LWR temperatures and assess whether grid spacers can mitigate the tens of millimeters of bowing that would otherwise be expected in ∼4 m long LWR components.

bowing↗
DOE OSTI2026

Advancing SiC clad fuel performance model: bridging micro- and macro-scale models and experimental validation

This report presents a workflow for advancing fuel performance modeling of SiC composite cladding for light-water reactors by linking microscale, experimental data-informed finite element analysis with rod-scale fuel performance codes such as BISON. The workflow uses X-ray computed tomography (XCT) to capture the actual geometry and processing-induced defects of as-fabricated SiC composite tube specimens, particularly porosity and wall-thickness variations, and converts the segmented XCT volumes into image-based finite element meshes for high fidelity structural analysis.

Koyanagi, Takaaki [Oak Ridge National Laboratory (↗
DOE OSTI2025

Supporting Fusion at the Idaho National Laboratory

The Fusion Safety Program at Idaho National Laboratory has supported efforts to develop magnetic and inertial confinement fusion energy devices for commercial energy power development since 1979. In addition to our DOE less than hazard category 3 tritium handling facility STAR, we also have unique capabilities such as an adaptation of the severe accident code MELCOR developed specifically for fusion, and integrated modeling capabilities using the MOOSE Finite Element Code. In this presentation, we cover our unique experimental capabilities for investigating tritium sorption, solubility and permeation including in molten salts. We also show the application of MELCOR-TMAP to predict thermal hydraulics and tritium migration in normal and accident conditions. Finally, we demonstrate high-fidelity modeling capabilities found within the open-source MOOSE finite element framework as well as fuel-cycle modeling using TMAP8.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

PDE-constrained high-order mesh optimization

Here, we present a novel framework for PDE-constrained r-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality metric and a measure of the accuracy of the PDE solution obtained via finite element discretization. The proposed formulation achieves optimized, well-defined high-order meshes by integrating mesh quality control, PDE solution accuracy, and robust gradient regularization. We adopt the Target-Matrix Optimization Paradigm to control geometric properties across the mesh, independent of the PDE of interest. To incorporate the accuracy of the PDE solution, we introduce error measures that control the finite element discretization error. The implicit dependence of these error measures on the mesh nodal positions is accurately captured by adjoint sensitivity analysis. Additionally, a convolution-based gradient regularization strategy is used to ensure stable and effective adaptation of high-order meshes. We demonstrate that the proposed framework can improve mesh quality and reduce the error by up to 10 times for the solution of Poisson and linear elasto-static problems. The approach is general with respect to the dimensionality, the order of the mesh, the types of mesh elements, and can be applied to any PDE that admits well-defined adjoint operators.

Computer science↗
DOE OSTI2025

Macro-micro multiscale modeling to assist the design of HPDC Al castings microstructure and alloys for EV super-large body structures (Phase 1)

Implementation of High Pressure Die Casting (HPDC) Aluminum (Al) body structures for high volume electrified vehicles (EV) to improve electric efficiency remains a key strategy within many original equipment manufacturer (OEM)s. In addition to high strength for safety requirements, superior Self-Piercing Riveting (SPR) performance is demanded for HPDC Al alloys to be compatible with high volume SPR joining. In this work, it is proposed to extend and validate an existing Contractor finite element multiscale macro-micro modeling approach to quantify the influence of the microstructure of HPDC alloys on the fracture strain/displacement under 3-point bend and clinch testing. The success of this work will allow to replace solution treatment stage with low energy consumption heat treatment (HT) processes, or to design new non heat treatable (NHT) HPDC Al alloys to eliminate HT requirements. Ultimately, this project will facilitate the application of HPDC Al alloys for super-large vehicle structures to significantly reduce vehicle weight, and thus improving energy efficiency. The purpose of this project is to extend and validate an existing finite element code, which is based on the Contractor developed macro-micro multi-scale modeling approach, to numerically simulate the three-point bending and clinch test and study the influences of material microstructural characteristics and phase properties on the rivetability. The macro-micro modeling approach begins with a sample scale model and identify the location, which is mostly prone to failure, the deformation history of the boundaries of that location calculated will be used to drive a microstructure-based sub-models where the material microstructure and microscale properties are considered. Using this approach, the wrap-bending failure for two Al alloys are correctly predicted for the first time. This will start with phase I effort of building a framework of macro-micro three point bending test and clinch test of Al10SiMgMn HPDC alloy in the as-cast and T7 heat treated conditions. Those results will then be validated with experimental test results. The phase II effort will involve the utilization of the knowledge learned in phase I to establish the quantitative correlation between the microstructure characteristics and the riveting performance, which will be further used to guide the optimization of HPDC Al alloy microstructure using heat treatment process to achieve sufficient rivetability to join large thin-wall HPDC alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Sprain energy consequences for damage localization and fracture mechanics

The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the “sprain,” as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ( C 0 ) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.

Science & Technology - Other Topics↗
DOE OSTI2024

Laser Shock Modeling Archival Discussion

The purpose of this discussion is to provide archival information related to the Laser Shock finite element modeling effort. As discussed in Laser Shock System, Assessing bond strength in layered materials (see Section 8.0), the Laser Shock System creates a high-amplitude shockwave on the frontside of a structure (i.e. an aluminum 6061-T6 plate for this discussion) via a high-energy pulsed laser. The shock wave is monitored on the back surface of the structure as a velocity time history. It is a compressive wave as it comes to the back surface but reflects as a tensile wave. If a bond exists in the structure and the reflected tensile wave exceeds its interface threshold stress, then bond rupture occurs. The desire of the Laser Shock effort is to establish (with multiple tests) an ultimate bond strength which can be used for fuel plate design calculations. In this process, the finite element modeling effort is the catalyst to mimic the Laser Shock tests and provide the damage information at the bond that is useful for fuel plate design calculations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Photo-oxidation of semicrystalline polymers: Effect of stress triaxiality on ductility

The effect of stress triaxiality on the strain-to-fracture of as-received and photo-oxidized polyamide-6 (PA-6) was investigated using mechanical testing, synchrotron X-ray tomography, and finite element analyses. Mechanical tests were conducted on cylindrical and round notched specimens, where different notch radii were used to vary the stress triaxiality. The specimens were aged by exposure to ultra-violet (UV) radiation at 60∘, causing photo-oxidation. As-received and so-aged specimens were loaded to failure (complete loss of load carrying capacity). For both unaged and aged specimens, a higher triaxiality led to a lower strain-to-fracture. To elucidate the micromechanical damage that mediates fracture in both conditions, specimens with an intermediate notch sharpness were loaded to the peak load, unloaded, and scanned ex situ using synchrotron X-ray tomography. Damage in the unaged bar was found to occur by cavitation and was concentrated at the center of the specimen, where the triaxiality is highest. In the UV-aged bar, a network of inter-connected chemical cracks were found on the notch surface, where the triaxiality is lowest. Finite element analyses were deployed to approximate the local triaxiality at damaged regions in the unaged and UV-aged specimens using a constitutive relation for semicrystalline polymers. From these analyses, the relationship between local triaxiality and strain-to-fracture was quantified for both unaged and photo-oxidized PA-6. Both unaged and photo-oxidized PA-6 showed similar decreases in ductility with triaxiality, hinting at common ductile fracture processes.

36 MATERIALS SCIENCE↗
DOE OSTI2025

TRUST Sensors in Environments: Thermocouples (SE-TC), Release FY25

The Delivery Environments Testbeds to Reduce Uncertainty in Simulations and Tests (TRUST) project is a broad project intended to analyze simplified problems experimentally and with modeling and simulation. The purpose of analyzing these simplified problems is to extend solution methods to more complex problems, as well as understand deficiencies and gaps in knowledge of methods currently used in more complex analyses. The TRUST project encompasses several smaller testbeds intended to isolate individual phenomena. The testbed under consideration in this report is the Sensors in Environments: Thermocouples testbed. In previous years, the purpose of this testbed was to quantify uncertainty of thermocouple sensors. To accomplish this, an aluminum plate was placed in a thermal chamber and subject to various types of thermal loading. Thermocouples were placed in various locations on the aluminum plate in various configurations (e.g., embedded in the plate, placed under Kapton tape), and an effort was made to quantify uncertainty in these measurements. Finite element simulations were performed to investigate how sensitive these measurements were to parameters such as the boundary conditions on the plate and material properties. However, a fundamental source of uncertainty in this analysis was the convective heat transfer from the plate. Convective heat transfer is a complex physical phenomenon comprised of a number of interacting sub-processes and is difficult to predict accurately a priori. As such, the main purpose of this testbed in FY25 was to better understand, both experimentally and numerically, the convective heat transfer from the plate. This is a highly applicable problem to several more complex problems, as convective heat transfer occurs in nearly all problems where a body is moving through air. Numerically, this required a two-step approach. First, the air flow in the thermal chamber was in vestigated using computational fluid dynamics. The commercial solver Fluent was used to perform these simulations. From these simulations, a heat transfer coefficient over the surface of the plate was calculated. This heat transfer was then used as boundary conditions for finite element heat transfer simulations within the plate, which were performed using Abaqus. Significant effort was devoted to automating the handoff between these two solvers. Experimentally, previous thermocouple results in the plate were used to validate the time-dependent thermal profiles produced from Abaqus. Further experimental efforts were performed both to help validate the Fluent simulations and to inform its boundary conditions. For example, hot-wire anemometers were used to measure the velocity in the chamber, which would be particularly useful in understanding the chamber inlet velocity. Thermocouple measurements were also taken in the chamber, instead of only on the plate, to serve as validation evidence for the Fluent simulations. Numerical results showed that the Fluent to Abaqus workflow matched previous plate thermocouple measurements well. This type of handoff is useful for more complex experiments, or those that are not able to be examined in as great of detail as this testbed, as it was performed without any experimental input. Experimental results, however, were more mixed. The anemometers proved unreliable, with inconsistent measurements across all anemometers, even at locations that were nearly identical. On the other hand, the thermocouples provided a relatively rich view of the temperature field in the chamber.

42 ENGINEERING↗
DOE OSTI2025

Solving high-dimensional partial integral differential equations: The finite expression method

Partial integro-differential equations (PIDEs) have broad applications in the sciences, from electro-magnetism to options pricing. Here, in this paper, we introduce a new finite expression method (FEX) to solve PIDEs. This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel method of parameter grouping is proposed to reduce the number of coefficients in high-dimensional function approximation; 2) A Taylor series approximation method is implemented to significantly improve the computational efficiency and accuracy of the evaluation of the integral terms of PIDEs. The new FEX based method, denoted FEX-PG to indicate the addition of the parameter grouping (PG) step to the algorithm, provides both high accuracy and interpretable numerical solutions, with the outcome being an explicit equation that facilitates intuitive understanding of the underlying solution structures. These features are often absent in traditional methods, such as finite element methods (FEM) and finite difference methods, as well as in deep learning-based approaches. To benchmark our method against recent advances, we apply the new FEX-PG to solve benchmark PIDEs in the literature. In high-dimensional settings, FEX-PG exhibits strong and robust performance, achieving relative errors on the order of single precision machine epsilon, significantly outperforming existing approaches based on neural networks.

Combinatorial optimization↗
DOE OSTI2025

Prelude to Simulation Diagnostics in MOOSE: Diagnosing Meshes

As finite element simulations increase in complexity, so does the need for high quality meshes. Without proper diagnostics, issues pertaining to poor mesh quality or improper mesh construction may go undetected, causing simulations to fail unexpectedly. This paper details the new mesh diagnostic system available in MOOSE, which provides users with the tools to inspect mesh quality for both externally and internally generated meshes. This system can detect issues arising from element volume size, non-conformal elements, intersecting edges, missing sidesets, as well as other common mesh issues. As meshes increase in size and complexity, such issues become more difficult to diagnose through visual inspection alone.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2026

Computational modeling of graphite degradation in molten salt reactors: Role of infiltration

Molten salt reactors (MSRs) often employ graphite as a moderator and reflector. An important challenge for deploying graphite in these reactors is that, due to limited experimental data, our understanding of graphite’s structural integrity in molten salt environments remains incomplete. Here, this study addresses heat generation from fuel-bearing salt that has infiltrated open pores in the graphite, driven primarily by pressure differentials. This is one of multiple identified physical and chemical mechanisms through which molten salt could potentially degrade graphite. Thermally driven stresses are quantified using the Molten-Salt Reactor Experiment (MSRE) graphite moderator elements as a case study. Finite element simulations predict stress distributions at varying infiltration levels, indicating that thermal stresses increase with higher infiltration. Rare-event simulations using the parallel subset simulation framework identify the combinations and corresponding ranges of input parameters that lead to stresses above a specified threshold. In particular, combinations involving high infiltration amounts, high power density, and low thermal conductivity tend to induce the highest stresses. Under the inputs and assumptions considered in this work, the magnitudes of the thermally driven stresses are quite low, with a very low likelihood of causing failure due to exceeding the graphite’s tensile strength. Additionally, rare-event simulations were performed for two more scenarios: a scaled-up moderator geometry and a localized hotspot in the original geometry. Both cases resulted in increased susceptibility to failure, though not to a detrimental extent. Furthermore, the combined effects of irradiation and infiltration-induced thermal stresses were evaluated. The results showed that thermal stresses from infiltration were negligible compared to those caused by irradiation. The findings of such a study are inherently component-specific, but the methodology presented here could be used for similar assessments of salt-infiltration effects in other graphite components.

36 - MATERIALS SCIENCE↗
DOE OSTI2025

A Parametric, Data-Driven, Non-Intrusive Reduced-Order Model Framework for Crystal Plasticity Simulations of Voids

The influence of the internal structure at micrometer length scales on the deformation of polycrystalline materials can be effectively captured using crystal plasticity finite element methods (CPFEM). However, the complexity and nonlinearity of the deformation equations CPFEM solves demand significant computational power and resources to achieve accurate predictions, limiting its broader application. To address this challenge, we have identified a reduced-order representation of the complex data in order to establish a computationally efficient reduced-order models (ROM) and drastically reduce the computational expense of CPFEM. Specifically, in this work, we developed a parametric, data-driven, and non-intrusive ROM framework for CPFEM using proper orthogonal decomposition (POD) and sparse variational Gaussian process (SVGP) regression for single-crystal microstructures under tensile loading conditions. The developed protocol enables one to compress field into a latent/low-dimensional space described by principal component analysis (PCA) via the singular value decomposition (SVD) algorithm. As a result, the high-dimensional data are reduced to a significantly smaller amount of dimensions with POD bases and POD coefficients. Furthermore, we deployed an ensemble of SVGPs—extended from the classical Gaussian process (GP) regression for scalability and handling big data—in a massively parallel manner to train and predict latent POD coefficients using known POD bases from a set of previously obtained simulations results. Lastly, using the predicted POD coefficients, we reconstructed the full-field results and showed reasonable agreement compared with the true values obtained from running CPFEM. The developed framework is validated with a set of CPFEM simulations of a single embedded void in single-crystal aluminum alloy. While the framework is broadly applicable, this work specifically focuses on single-crystal microstructures, a single load case (e.g., tensile), and a specific void geometry (spherical).

Anisotropy↗
DOE OSTI2025

A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.

Automatic differentiation↗