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Approximation of a Martensitic Laminate with Varying Volume Fractions

Published online by Cambridge University Press:  15 August 2002

Bo Li  and
Mitchell Luskin
Bo Li
Affiliation:
Department of Mathematics, University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90095-1555, USA.
Mitchell Luskin
Affiliation:
School of Mathematics, University of Minnesota, 206 Church Street, S.E., Minneapolis, MN 55455, USA.
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Abstract

We give results for the approximation of a laminate withvarying volume fractions for multi-well energy minimizationproblems modeling martensitic crystals thatcan undergo either an orthorhombicto monoclinic or a cubic to tetragonal transformation. We construct energy minimizing sequences of deformations which satisfythe corresponding boundary condition, and we establish a series of error bounds in terms of the elastic energyfor the approximation of the limiting macroscopicdeformation and the simply laminated microstructure.Finally, we give results for the corresponding finite element approximation of the laminate with varying volume fractions.

Keywords

martensitic transformationsimple laminatevolume fractionYoung measurefinite elementerror estimate
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 1 , January 1999 , pp. 67 - 87
Copyright
© EDP Sciences, SMAI, 1999

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