Volume 34, Number 3, May/june 2000
|Page(s)||663 - 685|
|Published online||15 April 2002|
Stability of microstructure for tetragonal to monoclinic martensitic transformations
School of Mathematics, University of Minnesota, 206 Church
Street SE, Minneapolis, MN 55455, USA;
2 School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, MN 55455, USA; (firstname.lastname@example.org)
Revised: 25 November 1999
We give an analysis of the stability and uniqueness of the simply laminated microstructure for all three tetragonal to monoclinic martensitic transformations. The energy density for tetragonal to monoclinic transformations has four rotationally invariant wells since the transformation has four variants. One of these tetragonal to monoclinic martensitic transformations corresponds to the shearing of the rectangular side, one corresponds to the shearing of the square base, and one corresponds to the shearing of the plane orthogonal to a diagonal in the square base. We show that the simply laminated microstructure is stable except for a class of special material parameters. In each case that the microstructure is stable, we derive error estimates for the finite element approximation.
Mathematics Subject Classification: 49J45 / 65N15 / 65N30 / 73C50 / 73G05 / 73K20 / 73V05
Key words: Martensitic transformation / microstructure / nonconvex variational problem / simple laminate / tetragonal / monoclinic / volume fraction / Young measure / finite element / error estimate
© EDP Sciences, SMAI, 2000
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