Unconditionally stable, second-order schemes for gradient-regularized, non-convex, finite-strain elasticity modeling martensitic phase transformations
- University of Michigan, Ann Arbor, MI (United States)
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.
- Research Organization:
- Univ. of Michigan, Ann Arbor, MI (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE); National Science Foundation (NSF); San Diego Supercomputer Center (SDSC); USDOE
- Grant/Contract Number:
- SC0008637; AC02-05CH11231; AC04-94AL85000; ACI-1548562
- OSTI ID:
- 1538124
- Alternate ID(s):
- OSTI ID: 1548214
- Journal Information:
- Computer Methods in Applied Mechanics and Engineering, Vol. 338, Issue C; ISSN 0045-7825
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures
|
journal | December 2020 |
| 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 |
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