TY - JOUR
T1 - The simply laminated micro structure in martensitic crystals that undergo a cubic-to-orthorhombic phase transformation
AU - Bhattacharya, Kaushik
AU - Li, Bo
AU - Luskin, Mitchell
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 1999/10/22
Y1 - 1999/10/22
N2 - 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.
AB - 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.
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U2 - 10.1007/s002050050170
DO - 10.1007/s002050050170
M3 - Article
AN - SCOPUS:0033437538
SN - 0003-9527
VL - 149
SP - 123
EP - 154
JO - Archive For Rational Mechanics And Analysis
JF - Archive For Rational Mechanics And Analysis
IS - 2
ER -