The Simply Laminated Microstructure in Martensitic Crystals that Undergo a Cubic-to-Orthorhombic Phase Transformation

Creators: Bhattacharya, Kaushik; Li, Bo; Luskin, Mitchell

Abstract

We study simply laminated microstructures of a martensitic crystal capable of undergoing a cubic‐to‐orthorhombic transformation of type P^((432))→P^((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.

Additional Information

© Springer-Verlag 1999. Accepted November 24, 1998. This paper was completed while Kaushik Bhattacharyawas visiting the Max-Planck Institute for Mathematics in the Sciences in Leipzig. He was grateful for the hospitality of the institute. He was also partially supported by the NSF through grant CMS-9457573 and by the AFOSR through grant F49620-95-1-0109. Bo Li was partially supported by the ARPA/URI/ONR through grant N00014-92-J-1890 and by the NSF through grant DMS 96-15854. Mitchell Luskin was partially supported by the NSF through grant DMS 95-05077, by the AFOSR through grant AF/F 49620-97-1-0187, and by a grant from the Minnesota Supercomputer Institute.

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The Simply Laminated Microstructure in Martensitic Crystals that Undergo a Cubic-to-Orthorhombic Phase Transformation

Abstract

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