Unconditionally stable, second-order schemes for gradient-regularized, non-convex, finite-strain elasticity modeling martensitic phase transformations
Abstract
In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for regularization. Metastable martensitic microstructures, defined as solutions that are local minimizers of the total free energy, are of interest and are obtained as steady state solutions to the resulting transient formulation of Toupin’s gradient elasticity at finite strain. This type of problem poses several numerical challenges including stiffness, the need for fine discretization to resolve microstructures, and following solution branches. Accurate time-integration schemes are essential to obtain meaningful solutions at reasonable computational cost. Here in this work we introduce two classes of unconditionally stable second-order time-integration schemes for gradient elasticity, each having relative advantages over the other. Numerical examples are shown highlighting these features.
- Authors:
-
- University of Michigan, Ann Arbor, MI (United States)
- Publication Date:
- Research Org.:
- Univ. of Michigan, Ann Arbor, MI (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE); National Science Foundation (NSF); San Diego Supercomputer Center (SDSC); USDOE
- OSTI Identifier:
- 1538124
- Alternate Identifier(s):
- OSTI ID: 1548214
- Grant/Contract Number:
- SC0008637; AC02-05CH11231; AC04-94AL85000; ACI-1548562
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Additional Journal Information:
- Journal Volume: 338; Journal Issue: C; Journal ID: ISSN 0045-7825
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; gradient elasticity; stability; martensitic phase transformation; twinning
Citation Formats
Sagiyama, K., and Garikipati, K. Unconditionally stable, second-order schemes for gradient-regularized, non-convex, finite-strain elasticity modeling martensitic phase transformations. United States: N. p., 2018.
Web. doi:10.1016/j.cma.2018.04.036.
Sagiyama, K., & Garikipati, K. Unconditionally stable, second-order schemes for gradient-regularized, non-convex, finite-strain elasticity modeling martensitic phase transformations. United States. https://doi.org/10.1016/j.cma.2018.04.036
Sagiyama, K., and Garikipati, K. Sat .
"Unconditionally stable, second-order schemes for gradient-regularized, non-convex, finite-strain elasticity modeling martensitic phase transformations". United States. https://doi.org/10.1016/j.cma.2018.04.036. https://www.osti.gov/servlets/purl/1538124.
@article{osti_1538124,
title = {Unconditionally stable, second-order schemes for gradient-regularized, non-convex, finite-strain elasticity modeling martensitic phase transformations},
author = {Sagiyama, K. and Garikipati, K.},
abstractNote = {In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for regularization. Metastable martensitic microstructures, defined as solutions that are local minimizers of the total free energy, are of interest and are obtained as steady state solutions to the resulting transient formulation of Toupin’s gradient elasticity at finite strain. This type of problem poses several numerical challenges including stiffness, the need for fine discretization to resolve microstructures, and following solution branches. Accurate time-integration schemes are essential to obtain meaningful solutions at reasonable computational cost. Here in this work we introduce two classes of unconditionally stable second-order time-integration schemes for gradient elasticity, each having relative advantages over the other. Numerical examples are shown highlighting these features.},
doi = {10.1016/j.cma.2018.04.036},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 338,
place = {United States},
year = {Sat May 05 00:00:00 EDT 2018},
month = {Sat May 05 00:00:00 EDT 2018}
}
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Works referencing / citing this record:
Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures
journal, December 2020
- Zhang, Xiaoxuan; Garikipati, Krishna
- Computer Methods in Applied Mechanics and Engineering, Vol. 372
Machine learning materials physics: Deep neural networks trained on elastic free energy data from martensitic microstructures predict homogenized stress fields with high accuracy
preprint, January 2019
- Sagiyama, K.; Garikipati, K.
- arXiv