A New Rock Salt Constitutive Model with Back Stress and Drag Stress Hardening.
Abstract not provided.
Reedlunn, Benjamin↗
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Results for “constitutive models”
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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↗
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↗
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↗
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↗
A Goal-oriented Approach to Model Form Error for Constitutive Models.
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Seidl, Daniel Thomas↗
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(10 2 −10 3 )s −1 ) and larger overpressure magnitudes (𝒪(10 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(10 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(10 2 −10 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↗
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↗
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↗
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↗
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.↗
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↗
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↗
An assessment of Callahan's crushed salt constitutive model
This memorandum investigates the Callahan crushed salt constitutive model developed and used at Sandia National Laboratories for geomechanics applications. The formulation is reviewed, calibration against a novel long-term experiment with complex loading history is performed and validation against other experiments is attempted. Areas of improvement and deficiencies are identified that support the need for an alternative or updated constitutive model for crushed salt.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities
Here, we present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.
42 ENGINEERING↗
Calibrating the SPECTACULAR constitutive model using legacy Sandia data for two filled epoxy systems: 828/CTBN/DEA/GMB and 828/DEA/GMB
The SPECTACULAR model is a development extension of the Simplified Potential Energy Clock (SPEC) model. Both models are nonlinear viscoelastic constitutive models used to predict a wide range of time-dependent behaviors in epoxies and other glass-forming materials. This report documents the procedures used to generate SPECTACULAR calibrations for two particulate-filled epoxy systems, 828/CTBN/DEA/GMB and 828/DEA/GMB. No previous SPECTACULAR or SPEC calibration exists for 828/CTBN/DEA/GMB, while a legacy SPEC calibration exists for 828/DEA/GMB. To generate the SPECTACULAR calibrations, a step-by-step procedure was executed to determine parameters in groups with minimal coupling between parameter groups. This procedure has often been deployed to calibrate SPEC, therefore the resulting SPECTACULAR calibration is backwards compatible with SPEC (i.e. none of the extensions specific to SPECTACULAR are used). The calibration procedure used legacy Sandia experimental data stored on the Polymer Properties Database website. The experiments used for calibration included shear master curves, isofrequency temperature sweeps under oscillatory shear, the bulk modulus at room temperature, the thermal strain during a temperature sweep, and compression through yield at multiple temperatures below the glass transition temperature. Overall, the calibrated models fit the experimental data remarkably well. However, the glassy shear modulus varies depending on the experiment used to calibrate it. For instance, the shear master curve, isofrequency temperature sweep under oscillatory shear, and the Young's modulus in glassy compression yield values for the glassy shear modulus at the reference temperature that vary by as much as 15 %. Also, for 828/CTBN/DEA/GMB, the temperature dependence of the glassy shear modulus when fit to the Young's modulus at different temperatures is approximately four times larger than when it is determined from the isofrequency temperature sweep under oscillatory shear. For 828/DEA/GMB, the temperature dependence of the shear modulus determined from the isofrequency temperature sweep under oscillatory shear accurately predicts the Young's modulus at different temperatures. When choosing values for the shear modulus, fitting the glassy compression data was prioritized. The new and legacy calibrations for 828/DEA/GMB are similar and appear to have been calibrated from the same data. However, the new calibration improves the fit to the thermal strain data. In addition to the standard calibrations, development calibrations were produced that take advantage of development features of SPECTACULAR , including an updated equilibrium Helmholtz free energy that eliminates undesirable behavior found in previous work. In addition to the previously mentioned experimental data, the development calibrations require data for the heat capacity during a stress-free temperature sweep to calibrate thermal terms.
36 MATERIALS SCIENCE↗
ASME Code Revisions to Incorporate 316H and Alloy 617 Viscoplastic Constitutive Models to Section III, Division 5 and Code Case N-898
This report provides a final status update on work to develop and implement two new constitutive models for 316H stainless steel and the Ni-based Alloy 617 in Nonmandatory Appendix Z to the Section III, Division 5, Subsection HB, Subpart B ASME Boiler & Pressure Vessel Code rules covering the design and construction of Class A high temperature nuclear reactor components. This report summarizes the objections of the overall project and provides the final versions of the constitutive models proposed for incorporation into the ASME Code. The report also provides an update on the balloting status at ASME of the two proposed constitutive models. As of the time of writing (July 2022) the models are on-track to be approved by ASME after the August 2022 Code Week. If so, this will mean the 316H model will be published in the 2023 edition of the Code and the A617 model available as part of a revised Code Case immediately
36 MATERIALS SCIENCE↗
Advancements in Constitutive Model Calibration: Leveraging the Power of Full‐Field DIC Measurements and In Situ Load Path Selection for Reliable Parameter Inference
Accurate material characterization and model calibration are essential for computationally supported high-consequence engineering decisions. Historically, characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data are collected for a specific model of interest, (3) use deterministic methods that provide best-fit parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work brings together several recent advancements into an improved workflow called interlaced characterization and calibration (ICC) that advances the state-of-the-art in constitutive model calibration. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) quantifies parameter uncertainty through Bayesian inference and (4) incorporates these advancements into a quasi real-time feedback loop. The ICC framework is demonstrated here on the calibration of a material model using simulated full-field data for an aluminium cruciform specimen being deformed biaxially. The cruciform is actively driven through the myopically preferred load path using Bayesian optimal experimental design, which selects load steps that yield the maximum expected information gain (EIG). Principal component analysis (PCA) is performed on the model predictions of full-field displacements, and fast surrogate models are built to approximate the input-output relationships of the expensive finite element model. Furthermore, the tools developed and demonstrated here show that high-fidelity constitutive models can be efficiently and reliably calibrated with quantified uncertainty, thus supporting credible decision-making and potentially increasing the agility of solid mechanics modelling by enabling utilization of computational simulations at earlier stages of the design cycle.
Bayesian optimal experimental design↗