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Results for “Constitutive modeling”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A constitutive model for sheared dense suspensions of rough particles

In a concentrated suspension, particles come into contact due to the presence of asperities on their surfaces. As a result, the contact forces and interparticle friction become one of the important factors governing the rheology of rigid particle suspensions at high concentrations. We show that a load-dependent friction model can be used to reproduce the experimentally observed shear thickening [ST—continuous and discontinuous (DST)] behavior with an increase in the asperity size. Increasing the particle surface roughness size leads to a decrease in the critical shear rate above which shear-thickening takes place, a reduction in the critical volume fraction for DST and an increase in the viscosity jump across non-shear-thickened to shear-thickened regime. In this paper, we propose a constitutive model to quantify the effect of increasing the roughness size on the rheology of dense ST suspensions as well as on the critical shear rate for ST and the critical volume fraction for DST. We fit this model to our simulation data for stress controlled shear flow of dense rough particle suspensions. Once the fitting is complete, these equations are used to predict exact volume fractions and shear stress values for transitions between three regimes on the shear stress-shear rate flow state diagram for different roughness values. Furthermore, the results of this study can be used to tune the particle surface roughness for manipulating the dense suspension rheology according to different applications.

42 ENGINEERING↗
DOE OSTI2023

An asynchronous parallel high-throughput model calibration framework for crystal plasticity finite element constitutive models

Crystal plasticity finite element model (CPFEM) is a powerful numerical simulation in the integrated computational materials engineering toolboxes that relates microstructures to homogenized materials properties and establishes the structure–property linkages in computational materials science. However, to establish the predictive capability, one needs to calibrate the underlying constitutive model, verify the solution and validate the model prediction against experimental data. Bayesian optimization (BO) has stood out as a gradient-free efficient global optimization algorithm that is capable of calibrating constitutive models for CPFEM. Here in this paper, we apply a recently developed asynchronous parallel constrained BO algorithm to calibrate phenomenological constitutive models for stainless steel 304 L, Tantalum, and Cantor high-entropy alloy.

304L stainless steel↗
DOE OSTI2021

High Strain-Rate Strength Experiments on Molybdenum for Constitutive Model Parameter Selection

The constitutive model parameters for molybdenum obtained from the Plansee supplier have been constrained via Strength-Stabilized Rayleigh-Taylor experiments performed at the Los Alamos Neutron Science Center. Previous Hopkinson-bar measurements have produced a degenerate family of constitutive model parameters proven in the low strain rate regime. The experiments presented here provide a constraint at strain rates from 10 4 –10 6 s -1 which is used to select a preferred set of parameters for high strain-rate applications. Further analysis is warranted including determining a global fit in parameter space using all available high and low strain-rate data available.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism

We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure–property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius–Duhem inequality. The kinetic framework employs a stress–strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model’s results showing good correlations.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism

We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure–property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius–Duhem inequality. The kinetic framework employs a stress–strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model’s results showing good correlations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Constitutive Model of Radiation Aging Effects in Filled Silicone Elastomers under Strain

Filled silicone elastomers, an essential component in many technological applications, are often subjected to controlled or unintended radiation for a variety of reasons. Radiation exposure can lead to permanent mechanical and structural changes in the material, which is manifested as altered mechanical response, and in some cases, a permanent set. For unfilled elastomers, network theories developed and refined over decades can explain these effects in terms of chain-scission and cross-link formation and a hypothesis involving independent networks formed at different strain levels of the material. In this work, we expose a filled silicone rubber to gamma radiation while being under finite elongational strain and show that the observed mechanical and structural changes can be quantitatively modeled within the same theoretical framework developed for unfilled elastomers as long as nuances associated with the Mullins effect are accounted for in a consistent manner. In this work, we employ Ogden’s incompressible hyperelastic model within the framework of Tobolsky’s two-network scheme to describe the observed permanent set and mechanical modulus changes as a function of radiation dosage. In the process, we conclude that gamma radiation induces both direct cross-linking at chain crossings (H-links) and main-chain-scission followed by cross-linking (Y-links). We provide an estimate of the ratio of chain-scission to cross-linking rates, which is in reasonable agreement with previous experimental estimate from Charlesby–Pinner analysis. We use density functional theory (DFT)-based quantum mechanical calculations to explore the stability of –Si and –SiO radicals that form upon a radiation-induced chain-scission event, which sheds light on the relative rates of Y-linking and H-linking processes.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Characteristics of Fluid‐Solid Interaction Constitutive Models Within Poroelastodynamics at Higher Strain‐Rates and Large Deformations Implemented in 1D

The large deformation, mixed formulation, finite element (FE) modeling approach presented in Irwin et al. 2024 is extended herein to include improved constitutive models for representing dynamic solid-fluid interactions at higher strain rates (𝒪⁢(1⁢0 2 −1⁢0 3 )⁢s −1 ) and larger overpressure magnitudes (𝒪⁡(1⁢0 2 )⁢kPa) within a biphasic soft porous material using Theory of Porous Media (TPM) at finite strain. Specifically, these constitutive modeling improvements are the following: (i) a more physically robust constitutive model for pore fluid seepage velocity via inclusion of pore fluid viscous stress, and (ii) a modified deformation-dependent-permeability model and updated hyperelastic constitutive model better suited for handling larger volumetric compressions and extensions. The novelty of the present work is mainly the contribution (i): inclusion of pore fluid viscous stress at higher strain-rate and large deformations, which requires 𝐶 1 continuity in the weak formulation, accomplished by employing Hermite cubic interpolation functions within a mixed nonlinear poromechanical finite element formulation. In (ii), the model is updated to weakly enforce solid phase incompressibility, such that this assumption is not violated numerically, which provides improved numerical stability for achieving larger overpressure magnitudes on 𝒪⁡(1⁢0 2 ) kPa, which were not achievable with the previous Kozeny–Carman model in Irwin et al. 2024. Also in (ii), the volumetric part of the solid skeleton free energy function is modified to ensure proper bounds on the solid skeleton Jacobian of deformation 𝐽 s related to incompressibility of the solid phase. Uniaxial strain, unidirectional flow examples at higher strain rates (𝒪⁢(1⁢0 2 −1⁢0 3 )⁢s −1 ) and larger deformations (up to 0.2 (or 20%) nominal axial strain) demonstrate the improved physical representation—and numerical stability—of these constitutive model improvements.

42 ENGINEERING↗
DOE OSTI2025

A comparison of surrogate constitutive models for viscoplastic creep simulation of HT-9 steel

Mechanistic microstructure-informed constitutive models for the mechanical response of polycrystals are a cornerstone of computational materials science. However, as these models become increasingly more complex – often involving coupled differential equations describing the effect of specific deformation modes – their associated computational costs can become prohibitive, particularly in optimization or uncertainty quantification tasks that require numerous model evaluations. To address this challenge, surrogate constitutive models that balance accuracy and computational efficiency are highly desirable. Data-driven surrogate models, that learn the constitutive relation directly from data, have emerged as a promising solution. In this work, we develop two local surrogate models for the viscoplastic response of a steel: a piecewise response surface method and a mixture of experts model. These surrogates are designed to adapt to complex material behavior, which may vary with material parameters or operating conditions. The surrogate constitutive models are applied to creep simulations of HT-9 steel, an alloy of considerable interest to the nuclear energy sector due to its high tolerance to radiation damage, using training data generated from viscoplastic self-consistent (VPSC) simulations. In conclusion, we define a set of test metrics to numerically assess the accuracy of our surrogate models for predicting viscoplastic material behavior, and show that the mixture of experts model outperforms the piecewise response surface method in terms of accuracy.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Microstructure-Sensitive Uncertainty Quantification for Crystal Plasticity Finite Element Constitutive Models Using Stochastic Collocation Methods

Uncertainty quantification (UQ) plays a major role in verification and validation for computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive experiments. Within the structure-property linkage, crystal plasticity finite element method (CPFEM) models have been widely used since they are one of a few ICME toolboxes that allows numerical predictions, providing the bridge from microstructure to materials properties and performances. Several constitutive models have been proposed in the last few decades to capture the mechanics and plasticity behavior of materials. While some UQ studies have been performed, the robustness and uncertainty of these constitutive models have not been rigorously established. In this work, we apply a stochastic collocation (SC) method, which is mathematically rigorous and has been widely used in the field of UQ, to quantify the uncertainty of three most commonly used constitutive models in CPFEM, namely phenomenological models (with and without twinning), and dislocation-density-based constitutive models, for three different types of crystal structures, namely face-centered cubic (fcc) copper (Cu), body-centered cubic (bcc) tungsten (W), and hexagonal close packing (hcp) magnesium (Mg). Our numerical results not only quantify the uncertainty of these constitutive models in stress-strain curve, but also analyze the global sensitivity of the underlying constitutive parameters with respect to the initial yield behavior, which may be helpful for robust constitutive model calibration works in the future.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Review: Inelastic Constitutive Modeling: Polycrystalline Materials

This article provides a literature review that details the development of inelastic constitutive modeling as it relates to polycrystalline materials. This review distinguishes between inelastic constitutive models that account for nonlinear behavior at the microstructural level, time-independent classic plasticity models, and time-dependent unified models. Particular emphasis is placed on understanding the underlying theoretical framework for unified viscoplasticity models where creep and classical plasticity behavior are considered the result of applied boundary conditions instead of separable rates representing distinct physical mechanisms. This article establishes a clear understanding of the advantages of the unified approach to improve material modeling. This review also discusses recent topics in constitutive modeling that offer new techniques that bridge the gap between the microstructure and the continuum.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Calibrating constitutive models with full‐field data via physics informed neural networks

Abstract The calibration of solid constitutive models with full‐field experimental data is a long‐standing challenge, especially in materials that undergo large deformations. In this paper, we propose a physics‐informed deep‐learning framework for the discovery of hyperelastic constitutive model parameterizations given full‐field surface displacement data and global force‐displacement data. Contrary to the majority of recent literature in this field, we work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. The approach presented in this paper is computationally efficient, suitable for irregular geometric domains, and readily ingests displacement data without the need for interpolation onto a computational grid. A selection of canonical hyperelastic material models suitable for different material classes is considered including the Neo–Hookean, Gent, and Blatz–Ko constitutive models as exemplars for general non‐linear elastic behaviour, elastomer behaviour with finite strain lock‐up, and compressible foam behaviour, respectively. We demonstrate that physics informed machine learning is an enabling technology and may shift the paradigm of how full‐field experimental data are utilized to calibrate constitutive models under finite deformations.

Hamel, Craig M.↗
DOE OSTI2020

Calibration and modification of the constitutive model for the mechanical response of P91

The objective of this first milestone was to calibrate and if necessary, modify a constitutive model predicting the primary and secondary creep response of P91. The overall path to be followed consists of first calibrating this constitutive model against experimental data available from the literature (this milestone). In parallel, data acquired by indentation tests will be used to calibrate the model (this involves transforming the indentation data into equivalent uniaxial tests). An overall comparison of model parameters will allow assessing to what extent these rapid tests can be used to calibrate models predicting the overall mechanical response of the bulk. Given that COVID naturally hindered the gathering of new experimental data, the choice was made to ensure that LANL would have sufficient funds in year two to perform the bulk of the new calibration work. The following report details (i) how and which of the bulk experimental data was selected, (ii) constitutive model formulation, (iii) predictions of the constitutive model: effects of imposed stress, temperature and precipitate content, (iv) future work.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Constitutive Models via Automatic Differentiation v.1.0.0

SAND2024-00905O Constitutive Models via Automatic Differentiation (CMAD) provides a software framework for solving constitutive or material model calibration problems. It relies on JAX's automatic differentiation capabilities to compute the derivatives needed for both forward and adjoint sensitivity analyses. The software can be used to implement constitutive models and calibrate the parameters from experimental data. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Seidl, Daniel↗
DOE OSTI2020

Calibration of hyperelastic constitutive models: the role of boundary conditions, search algorithms, and experimental variability

The calibration of hyperelastic constitutive models of soft tissue and tissue surrogates is often treated as an exercise in curve-fitting to the average experimental response, and many of the complicating factors such as experimental boundary conditions and data variability are ignored. Here, we focus on three questions that arise in this area: the ramifications of ignoring the experimental boundary conditions, the use of local optimizers, and the role of data variability. Using data from a uniaxial extension experiment on a tissue surrogate, we study how these three factors affect the calibration of isotropic hyperelastic constitutive models. Our results show that even with the simplest of constitutive models, it is necessary to look beyond a "good fit" to the average.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

ASME Code change proposal to implement new universal high temperature constitutive models for Section III, Division 5

This report completes work on a universal high temperature constitutive model suitable for use with the ASME Boiler & Pressure Vessel Code Section III, Division 5 rules for the design by inelastic analysis of Class A nuclear reactor components. The goals of this work are to provide a simple model form that adequately captures the high temperature response of materials and can be applied to any future Code material. Additionally, the report describes an automated process for calibrating a model against test data. The idea is to simplify the effort required to generate a constitutive model for an arbitrary material, provided test data is available. This will accelerate the process of qualifying new Code materials in the future. In addition, the report provides calibrated models and detailed validation comparisons to test data for five currently-qualified or soon-to-be qualified materials: 316H, Grade 91, Alloy 800H, Alloy 617, and Alloy 709. The report surveys the available data for the remaining two ASME Class Materials --- 2.25Cr-1Mo and 304H --- concluding that there is enough data data to generate a model for 2.25Cr-1Mo steel provided some additional sources of non-public data can be included in the test database, but that a dedicated cyclic test campaign would be needed for 304H. Supplemental material includes the full text of an ASME Code change proposal to incorporate the models for the four currently-qualified Class A material, detailed validation comparisons to test data for the five material models, and input files for reference implementations of the constitutive models in the NEML and NEML2 modeling frameworks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗