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Stability of microstructure for tetragonal to monoclinic martensitic transformations

Published online by Cambridge University Press:  15 April 2002

Pavel Belik  and
Mitchell Luskin
Pavel Belik
Affiliation:
School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, MN 55455, USA; (belik@math.umn.edu)
Mitchell Luskin
Affiliation:
School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, MN 55455, USA; (luskin@math.umn.edu)
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Abstract

We give an analysis of the stability and uniqueness of the simplylaminated microstructure for all three tetragonal to monoclinicmartensitic transformations. The energy density for tetragonal tomonoclinic transformations has four rotationally invariant wells sincethe transformation has four variants. One of these tetragonal tomonoclinic martensitic transformations corresponds to the shearing ofthe rectangular side, one corresponds to the shearing of the squarebase, and one corresponds to the shearing of the plane orthogonal to adiagonal in the square base. We show that the simply laminatedmicrostructure is stable except for a class of special materialparameters. In each case that the microstructure is stable, we deriveerror estimates for the finite element approximation.

Keywords

Martensitic transformationmicrostructurenonconvex variational problemsimple laminatetetragonalmonoclinicvolume fractionYoung measurefinite elementerror estimate
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 3 , May 2000 , pp. 663 - 685
Copyright
© EDP Sciences, SMAI, 2000

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