Unconditionally stable, second-order accurate schemes for solid state phase transformations driven by mechano-chemical spinodal decomposition

Sagiyama, Koki; Rudraraju, Shiva; Garikipati, Krishna

doi:10.1016/j.cma.2016.09.003

Title: Unconditionally stable, second-order accurate schemes for solid state phase transformations driven by mechano-chemical spinodal decomposition

Journal Article · Tue Sep 13 00:00:00 EDT 2016 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2016.09.003· OSTI ID:1324034

Sagiyama, Koki ^[1]; Rudraraju, Shiva ^[1]; Garikipati, Krishna ^[1]

Univ. of Michigan, Ann Arbor, MI (United States)

Here, we consider solid state phase transformations that are caused by free energy densities with domains of non-convexity in strain-composition space; we refer to the non-convex domains as mechano-chemical spinodals. The non-convexity with respect to composition and strain causes segregation into phases with different crystal structures. We work on an existing model that couples the classical Cahn-Hilliard model with Toupin’s theory of gradient elasticity at finite strains. Both systems are represented by fourth-order, nonlinear, partial differential equations. The goal of this work is to develop unconditionally stable, second-order accurate time-integration schemes, motivated by the need to carry out large scale computations of dynamically evolving microstructures in three dimensions. We also introduce reduced formulations naturally derived from these proposed schemes for faster computations that are still second-order accurate. Although our method is developed and analyzed here for a specific class of mechano-chemical problems, one can readily apply the same method to develop unconditionally stable, second-order accurate schemes for any problems for which free energy density functions are multivariate polynomials of solution components and component gradients. Apart from an analysis and construction of methods, we present a suite of numerical results that demonstrate the schemes in action.

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Research Organization:: Univ. of Michigan, Ann Arbor, MI (United States). PRedictive Integrated Structural Materials Science (PRISMS) Center

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0008637

OSTI ID:: 1324034

Alternate ID(s):: OSTI ID: 1399034

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 10 works

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PRISMS: An Integrated, Open-Source Framework for Accelerating Predictive Structural Materials Science Aagesen, L. K.; Adams, J. F.; Allison, J. E. JOM, Vol. 70, Issue 10 https://doi.org/10.1007/s11837-018-3079-6	journal	August 2018
Verification of Convergence Rates of Numerical Solutions for Parabolic Equations Jeong, Darae; Li, Yibao; Lee, Chaeyoung Mathematical Problems in Engineering, Vol. 2019 https://doi.org/10.1155/2019/8152136	journal	June 2019
On the Thermodynamics of the Swift-Hohenberg Theory Espath, Lfr; Sarmiento, Af; Dalcin, L. arXiv https://doi.org/10.48550/arxiv.1610.00180	text	January 2016

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