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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A Three-Dimensional, Thermodynamically and Variationally Consistent, Fully Coupled, Electro-Chemo-Thermo-Mechanical Model of Solid-State Batteries

Here we present a theoretical framework for high fidelity modeling of three-dimensional electro-chemo-thermo-mechanical coupled systems such as solid-state batteries. The framework provides a useful means of utilizing molecular level information to predict the overall performance of the system at the continuum level. The central statement of the theoretical framework is a thermodynamically consistent inf-sup problem. The total potential of the coupled system consists of the Helmholtz free energy, the electrical kinetic potential, the chemical potential, the Fourier potential, the chemical reaction potential, and the external power expenditure. All governing equations derive from variational principles. We also show that the resulting initial-boundary-value problem (IBVP) is consistent with existing, widely adopted equations for modeling batteries. Moreover, the IBVP can be naturally discretized using the (variational) finite element method to simulate practical solid-state batteries with arbitrary geometries. Several examples illustrate multiphysics coupling between pairs of the physical field equations, culminating in a comprehensive three-dimensional model of charge-discharge in a solid state battery.

25 ENERGY STORAGE↗
DOE OSTI2023

Implementation and verification of a user-defined element (UEL) for coupled thermal-hydraulic-mechanical-chemical (THMC) processes in saturated geological media

Efficient and accurate modeling of the coupled thermal-hydraulic-mechanical-chemical (THMC) processes in various rock formations is indispensable for designing energy geo-structures such as underground repositories for high-level nuclear wastes. Here, this work focuses on developing and verifying an implicit finite element solver for generic coupled THMC problems in geological settings. Starting from the mass, momentum, and energy balance laws, a specialized set of governing equations and a thermoporoelastic constitutive model is derived. This system is then solved by an implicit finite element (FE) scheme. Specifically, the residuals and the Jacobians are scripted in a user-defined element (UEL) subroutine which is then combined with the general-purpose FE software Abaqus Standard to solve initial-boundary value problems. Considering the complexity of the system, the UEL development follows a stepwise manner by first solving the coupled hydraulic-mechanical (HM) and thermal-hydraulic-mechanical (THM) equations before moving on to the full THMC problem. Each implementation step consists of at least one verification test by comparing computed results with closed-form analytical solutions to ensure that the various coupling effects are correctly realized. To demonstrate the robustness of the algorithm and to validate the UEL, a three-dimensional case study is performed with reference to the in-situ heating test of ATLAS at Belgium in 1980s. A hypothetical radionuclide leakage event is then simulated by activating the chemical-concentration degree of freedom and prescribing a constant high concentration at the heater's surface. The model predicts a limited contaminated regime after six years considering both diffusion and advection effects on species transport.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

An finite element analysis surrogate model with boundary oriented graph embedding approach for rapid design

Abstract In this work, we present a boundary oriented graph embedding (BOGE) approach for the graph neural network to assist in rapid design and digital prototyping. The cantilever beam problem has been solved as an example to validate its potential of providing physical field results and optimized designs using only 10 ms. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed unstructured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based finite element analysis (FEA) results, which cannot be realized by other machine-learning-based surrogate methods. It has the potential to serve as a surrogate model for other boundary value problems. Focusing on the cantilever beam problem, the BOGE approach with 3-layer DeepGCN model achieves the regression with mean square error (MSE) of 0.011 706 (2.41% mean absolute percentage error) for stress field prediction and 0.002 735 MSE (with 1.58% elements having error larger than 0.01) for topological optimization. The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and Computer Aided Design (CAD) design-related areas.

42 ENGINEERING↗
DOE OSTI2022

A model of thermal creep and annealing in finite domains based on coupled dislocation climb and vacancy diffusion

Here, we develop a framework to investigate thermal creep and annealing in finite domains, where the climb motion of discrete dislocations is coupled to the diffusion of a continuum vacancy field. The model is first formulated in a continuum finite-deformation setting. All governing equations and boundary conditions are obtained from a unified irreversible thermodynamics principle. The resulting model couples a mechanical boundary value problem (BVP), a vacancy diffusion BVP, and the climb and glide motion of the discrete dislocation network within the crystal. The framework is then linearized for implementation in three-dimensional (3D) discrete dislocation dynamics (DDD) simulations for arbitrary anisotropic crystals. A solution scheme is developed based on the superposition principle, which is imposed weakly on the dislocation network to obtain a Galerkin solution for the nodal climb velocities. The framework includes diffusional (Nabarro–Herring) creep deformation as well as dislocation creep by climb-assisted-glide. The method is applied to simulate the annealing of vacancy loops in Al, with good agreement to experimental measurements by Silcox and Hirsch. We further consider the effects of annealing under stress, and of the proximity of the vacancy loops to loaded and free boundaries Simulations in polycrystalline materials are carried out to highlight the effects of the grain size on dislocation climb and vacancy loop annealing. The method is also applied to estimate the creep rate due to climb-assisted glide of jogged-screw dislocations in γ-TiAl, and results are compared to experiments by Viswanathan et al. Finally, we discuss the effects of uniaxial and hydrostatic stresses on the two diffusive deformation pathways of the material, namely Nabarro–Herring creep and dislocation climb.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Machine Learning Aided Modeling of Granular Materials: A Review

Artificial intelligence (AI) has become a buzzy word since Google’s AlphaGo beat a world champion in 2017. In the past five years, machine learning as a subset of the broader category of AI has obtained considerable attention in the research community of granular materials. This work offers a detailed review of the recent advances in machine learning-aided studies of granular materials from the particle-particle interaction at the grain level to the macroscopic simulations of granular flow. This work will start with the application of machine learning in the microscopic particle-particle interaction and associated contact models. Then, different neural networks for learning the constitutive behaviour of granular materials will be reviewed and compared. Finally, the macroscopic simulations of practical engineering or boundary value problems based on the combination of neural networks and numerical methods are discussed. We hope readers will have a clear idea of the development of machine learning-aided modelling of granular materials via this comprehensive review work.

42 ENGINEERING↗
DOE OSTI2026

A meshing framework for digital twins for extrusion based additive manufacturing

Additive manufacturing (AM) allows for manufacturing of complex three-dimensional geometries not typically realizable with standard manufacturing practices. The internal microstructure of AM components has a significant impact on mechanical, vibrational, and shock properties and permits richer design space when this is controllable. Due to complex interactions of internal geometry of an extrusion-based AM component, it is common practice to assume homogeneous behavior or to perform characterization testing on specific toolpath configurations. To avoid testing or material waste, it is necessary to develop a consistently accurate numerical simulation framework with relevant boundary value problems that can handle the complicated geometry of internal material microstructure present in AM components. Herein, a framework is proposed to directly create computational meshes suitable for finite element analysis (FEA) of the fine-scale features generated from extrusion-based AM tool paths to maintain a strong process–structure–property-performance linkage. This mesh can be manually or automatically analyzed using standard FEA simulations such as quasi-static preloading or modal analysis. The framework allows an in-silico assessment of a target AM geometry where fine-scale features greatly impact quantities of design interest such as in soft elastomeric lattices where toolpath infill can greatly influence the self-contact of a structure in compression, which we use as a motivating exemplar. This approach greatly reduces both time and resource waste present in traditional build and test design cycles for non-intuitive design spaces, and acts as a tool for use in the production of a key component of a digital twin, a mesh suitable for finite element analysis. In conclusion, it also further allows for the exploration of toolpath infill to optimize component properties beyond simple linear properties such as density and stiffness.

Additive manufacturing↗
DOE OSTI2024

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization

Here we develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets

A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary value problems described by partial differential equations (PDEs) for which a stochastic computational model (SCM) is available and which depend on a vector-valued random control parameter. The cost of a single numerical evaluation of this SCM is assumed to be such that only a limited number of points can be computed for constructing the training dataset (small data). Each point of the training dataset is made up of realizations from a vector-valued stochastic process (the stochastic solution) and the associated random control parameter on which it depends. The presented PLoM constrained by PDE allows for generating a large number of learned realizations of the stochastic process and its corresponding random control parameter. These learned realizations are generated so as to minimize the vector-valued random residual of the PDE in the mean-square sense. Appropriate novel methods are developed to solve this challenging problem. Three applications are presented. The first one is a simple uncertain nonlinear dynamical system with a nonstationary stochastic excitation. The second one concerns the 2D nonlinear unsteady Navier–Stokes equations for incompressible flows in which the Reynolds number is the random control parameter. Here, the last one deals with the nonlinear dynamics of a 3D elastic structure with uncertainties. The results obtained make it possible to validate the PLoM constrained by stochastic PDE but also provide further validation of the PLoM without constraint.

Machine learning↗
DOE OSTI2021

Anisotropic elastoplastic response of double-porosity media

Here we present a continuum framework to simulate fluid flow through anisotropic elastoplastic media with double porosity. Two effective stress measures σ' and δ" emerge from the thermodynamic formulation, which are energy-conjugate to the elastic and plastic components of strain, respectively. Both effective stress measures can be expressed as a combination of the total Cauchy stress σ and the average pore pressure $\bar{p}$ in the two pore scales. In the effective stress for elasticity, $\bar{p}$ is scaled with a rank-2 Biot tensor, whereas the effective stress for plasticity follows the Terzaghi form in which $\bar{p}$ is scaled by the Kronecker delta. The Biot tensor and storage coefficients are derived as functions of elasticity parameters and porosities. A mixed finite element formulation is introduced to discretize the domain and solve initial boundary-value problems. A stabilization scheme is employed on equal-order interpolation for both displacement and pressure fields throughout the entire range of drainage responses. Numerical simulations reproduce the hydromechanical response of Opalinus shale in one-dimensional consolidation tests throughout the range of primary and secondary consolidation under different external loads. Numerical simulations of the consolidation of a rectangular domain subjected to a strip load demonstrate the efficacy of the proposed stabilization scheme, as well as illustrate the impacts of stress history, mass transfer, and different pore systems on the hydromechanical response.

42 ENGINEERING↗
DOE OSTI2024

Three-dimensional continuum point cloud method for large deformation and its verification

This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Lastly, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.

Compressible neo-Hookean materials↗
DOE OSTI2022

Crystal plasticity modeling of strain-induced martensitic transformations to predict strain rate and temperature sensitive behavior of 304 L steels: Applications to tension, compression, torsion, and impact

This paper advances crystallographically-based Olson-Cohen (direct γ → α’) and deformation mechanism (indirect γ→ε→α’) phase transformation models for predicting strain-induced austenite to martensite transformation. Here, the advanced transformation models enable predictions of not only strain-path sensitive, but also of strain-rate and temperature sensitive deformation of polycrystalline stainless steels (SSs). The deformation of constituent grains in SSs is modeled as a combination of anisotropic elasticity, crystallographic slip, and phase transformation, while the hardening is based on the evolution of dislocation density and explicit shifts in phase fractions. Such grain-scale deformation is implemented within the meso-scale elasto-plastic self-consistent (EPSC) homogenization model, which is coupled with the implicit finite element (FE) method to provide a constitutive response at each FE integration point for solving boundary value problems at the macro-scale. Parameters pertaining to the hardening and transformation models within FEEPSC are calibrated and validated on a suite of data including flow curves and phase fractions for monotonic compression, tension, and torsion as a function of strain-rate and temperature for wrought and additively manufactured (AM) SS304L. To illustrate the potential and accuracy of the integrated multi-level FE-EPSC simulation framework, geometry, mechanical response, phase fractions, and texture evolution are simulated during gas-gun impact deformation of a cylinder and quasi-static tension of a notched specimen made of AM SS304L. Details of the simulation framework, comparison between experimental and simulation results, and insights from the results are presented and discussed.

304L steels↗
DOE OSTI2025

A generalizable machine learning-assisted fast Fourier transform algorithm to simulate the large strain phenomena in polycrystalline materials

Machine learning methods have shown initial promise in constitutive modeling for single crystals or homogenized polycrystals, delivering notable computational efficiency. However, existing machine learning-based constitutive models often lack generalizability, limiting their application across diverse boundary value problems. This study introduces a thermodynamics-informed artificial neural network model to accelerate rate-tangent crystal plasticity fast Fourier transform simulations for cross-scale deformation behaviors of polycrystals under complex loading. Our model integrates microstructural variability and local interactions effectively. To address local effects in each grain, we employ K-means clustering to group Gauss points within the microstructure into clusters assumed to be in similar mechanical states. This approach, based on self-clustering analysis, extends model scope from macroscopic stress response to the granular level, capturing mechanical responses and orientation evolution across grains. This reduces the number of nonlinear problems to solve, with cluster responses propagated throughout each group. The thermodynamics-based artificial neural network-extracted features are further processed using local material state clusters to account for history-dependent deformation and evolving microstructures. Additionally, representative volume element simulations with rate-tangent crystal plasticity fast Fourier transform provide reliable datasets for model training. The proposed model demonstrates high efficiency, accuracy, self-consistency, and enhanced generalizability in predicting strain–stress responses and orientation evolution at both individual grain and aggregate scales under complex loading conditions, such as biaxial tension and arbitrary loading scenarios.

36 MATERIALS SCIENCE↗
DOE OSTI2022

First-passage time statistics on surfaces of general shape: Surface PDE solvers using Generalized Moving Least Squares (GMLS)

Here, we develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics d X t = a (X t ) dt + b(X t ) d W t . We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form u (x) = E x [$∫^{τ}_{0}$ g (X t ) dt ] + E x [ f (X τ )] for a domain Ω and the exit stopping time τ = inf t { t >0 | X i Ω}, where f , g are general smooth functions. For computing these statistics, we develop high-order Generalized Moving Least Squares (GMLS) solvers for associated surface PDE boundary-value problems based on Backward- Kolmogorov equations. We focus particularly on the mean First Passage Times (FPTs) given by the case f = 0, g = 1 where u (x) = E x [τ]. We perform studies for a variety of shapes showing our methods converge with high-order accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how statistics are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation

In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a large class of computational models, it is possible to develop a computationally inexpensive procedure for calibrating parameters of high-fidelity models of physical events when the parameters of low-fidelity (surrogate) models are known with acceptable accuracy. The main ingredients in the proposed model calibration scheme are goal-oriented a-posteriori estimates of error in QoIs computed using a so-called lower fidelity model compared to those of an uncalibrated higher fidelity model. The estimates of error in QoIs are used to define likelihood functions in Bayesian inversion analysis. A standard Bayesian approach is employed to compute the posterior distribution of model parameters of high-fidelity models. As applications, parameters in a quasi-linear second-order elliptic boundary-value problem (BVP) are calibrated using a second-order linear elliptic BVP. In a second application, parameters of a tumor growth model involving nonlinear time-dependent PDEs are calibrated using a lower fidelity linear tumor growth model with known parameter values.

A-posterior estimates↗
DOE OSTI2024

Fast permeability measurement for tight reservoir cores using only initial data of the one chamber pressure pulse decay test

Here, in this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the upstream chamber are derived based on a parabolic arc approximation of pore pressure distribution along the test specimen. This approximation allows converting the initial–boundary value problem of fluid diffusion in the specimen, governed by partial differential equations, to a system of ordinary differential equations that can be easily solved by explicit formulae. Thus, an explicit formula for the pressure decay rate is obtained, which enables inverse analysis of the initial experimental data to estimate the rock permeability. The proposed method expedites the pulse decay test as it does not require the system to reach equilibrium. The method is validated with three sets of experimental data of the OC-PPD test using helium as the diffusing fluid, for which the relative error of the permeability is found to be less than 6%. This method is particularly useful if the equilibrium time of the pulse decay test for rock specimens with permeabilities in the range of nano-Darcy takes hours or days.

early-time solution↗
DOE OSTI2023

Benchmarking magnetised three-wave coupling for laser backscattering: analytic solutions and kinetic simulations

Understanding magnetised laser–plasma interactions is important for controlling magneto-inertial fusion experiments and developing magnetically assisted radiation and particle sources. For nanosecond pulses at non-relativistic intensities, interactions are dominated by coherent three-wave interactions, whose nonlinear coupling coefficients became known only recently when waves propagate at oblique angles with the magnetic field. In this paper, backscattering coupling coefficients predicted by warm-fluid theory are benchmarked using particle-in-cell simulations in one spatial dimension, and excellent agreements are found for a wide range of plasma temperatures, magnetic field strengths and laser propagation angles, when the interactions are mediated by electron-dominant hybrid waves. Systematic comparisons between theory and simulations are made possible by a rigorous protocol. On the theory side, the initial boundary value problem of linearised three-wave equations is solved, and the transient-time solutions allow the effects of growth and damping to be distinguished. On the simulation side, parameters are carefully chosen and calibration runs are performed to ensure that comparisons are well controlled. Fitting simulation data to analytical solutions yields numerical growth rates that match theory predictions within error bars. Although warm-fluid theory is found to be valid for a wide parameter range, genuine kinetic effects have also been observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Constructing field-aligned coordinate systems for gyrokinetic simulations of tokamaks in X-point geometries

Structures in tokamak plasmas are elongated along the direction of the magnetic field and short in the directions perpendicular to the magnetic field. Many tokamak simulation codes take advantage of this by using a field-aligned coordinate system. However, field-aligned coordinate systems have a coordinate singularity at magnetic X-points where the poloidal magnetic field vanishes, which makes it difficult to use field-aligned coordinate systems when simulating the core and scrape-off layer simultaneously. Here, we present an algorithm for grid generation and computing geometric quantities in a standard field-aligned coordinate system that avoids the singularity and allows one to conduct two-dimensional gyrokinetic axisymmetric simulations in X-point geometries. Convergence tests of advection, boundary value problems and geometric quantities all show greater than first-order convergence even in the vicinity of the X-point. We also demonstrate the geometric consistency of our algorithm with an example simulation of the spherical tokamak for energy production, which shows machine-precision particle conservation.

fusion plasma↗
DOE OSTI2022

Statistics of internal stress fluctuations in dislocated crystals and relevance to density-based dislocation dynamics models

A statistical analysis of internal stress fluctuations, defined as the difference between the local mean stress and stress on dislocations, is presented for deforming crystals with 3D discrete dislocation systems. Dislocation realizations are generated using dislocation dynamics simulations and the associated stress field is computed as a superposition of a regularized stress field of dislocation lines within the domain of the solution and a complementary stress field computed via a finite-element boundary value problem. The internal stress fluctuations of interest are defined by an ensemble of the difference between the stress on dislocation lines and the local mean field stress in the crystal. The latter is established in a piecewise fashion over small voxels in the crystal thus allowing the difference between the local average stress and stress on segments to be easily estimated. The results show that the Schmid stress (resolved shear stress) and Escaig stress fluctuations on various slip systems sampled over a random set of points follow a Cauchy (Lorentz) distribution at all strain levels, with the amplitude and width of the distribution being dependent on the strain. Finally, the implications of the Schmid and Escaig internal stress fluctuations are discussed from the points of view of dislocation cross-slip and the dislocation motion in continuum dislocation dynamics.

36 MATERIALS SCIENCE↗