Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

Kang, Ziliang; Tortorelli, Daniel A.; James, Kai A.

doi:10.1016/j.cma.2021.114364

Title: Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

Journal Article · Sat Dec 18 00:00:00 UTC 2021 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2021.114364 · OSTI ID:1867536

^[1]; Tortorelli, Daniel A. ^[2]; James, Kai A. ^[3]

Univ. of Illinois at Urbana-Champaign, IL (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Harvard Medical School, Boston, MA (United States)
Univ. of Illinois at Urbana-Champaign, IL (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of Illinois at Urbana-Champaign, IL (United States)

Here, we present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to resolve. Finite element analysis methods, which rely on Gauss quadrature integration schemes, must solve two sets of coupled differential equations: one at the global level and the other at the local, i.e. Gauss point level. In contrast to the conventional return mapping algorithm, which solves these two sets of coupled differential equations separately using a nested Newton procedure, we propose a scheme to solve the local and global differential equations simultaneously. In the process we also derive closed-form expressions used to update the internal/constitutive state variables, and unify the popular closest-point and cutting plane methods with our formulas. Numerical testing indicates that our method allows for larger thermomechanical loading steps and provides increased computational efficiency, over the standard return mapping algorithm.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: National Science Foundation; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1867536

Report Number(s):: LLNL-JRNL-822807; 1033475

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 389; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

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