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

Bhattacharya, Kaushik and Li, Bo and Luskin, Mitchell (1999) The Simply Laminated Microstructure in Martensitic Crystals that Undergo a Cubic-to-Orthorhombic Phase Transformation. Archive for Rational Mechanics and Analysis, 149 (2). pp. 123-154. ISSN 0003-9527. https://resolver.caltech.edu/CaltechAUTHORS:20131009-110131372

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://link.springer.com/article/10.1007%2Fs002050050170PublisherArticle
http://dx.doi.org/10.1007/s002050050170DOIArticle
ORCID:
AuthorORCID
Bhattacharya, Kaushik0000-0003-2908-5469
Li, Bo0000-0002-8019-8891
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.
Funders:
Funding AgencyGrant Number
NSFCMS-9457573
Air Force Office of Scientific Research (AFOSR)F49620-95-1-0109
Office of Naval Research (ONR)N00014-92-J-1890
NSFDMS 96-15854
NSFDMS 95-05077
Air Force Office of Scientific Research (AFOSR)AF/F 49620-97-1-0187
Minnesota Supercomputer InstituteUNSPECIFIED
Advanced Research Projects Agency (ARPA)UNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20131009-110131372
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20131009-110131372
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41809
Collection:CaltechAUTHORS
Deposited By: John Wade
Deposited On:09 Oct 2013 20:19
Last Modified:09 Mar 2020 13:19

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