The simply laminated micro structure in martensitic crystals that undergo a cubic-to-orthorhombic phase transformation

Kaushik Bhattacharya, Bo Li, Mitchell Luskin

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30 Scopus citations

Abstract

We study simply laminated microstructures of a martensitic crystal capable of undergoing a cubic-to-orthorhombic transformation of type ℘(432) → ℘(222)′. The free energy density modeling such a crystal is minimized on six energy wells that are pairwise rank-one connected. We consider the energy minimization problem with Dirichlet boundary data compatible with an arbitrary but fixed simple laminate. We first show that for all but a few isolated values of transformation strains, this problem has a unique Young measure solution solely characterized by the boundary data that represents the simply laminated microstructure. We then present a theory of stability for such a microstructure, and apply it to the conforming finite element approximation to obtain the corresponding error estimates for the finite element energy minimizers.

Original languageEnglish (US)
Pages (from-to)123-154
Number of pages32
JournalArchive For Rational Mechanics And Analysis
Volume149
Issue number2
DOIs
StatePublished - Oct 22 1999

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