Issue |
ESAIM: M2AN
Volume 34, Number 3, May/june 2000
|
|
---|---|---|
Page(s) | 663 - 685 | |
DOI | https://doi.org/10.1051/m2an:2000161 | |
Published online | 15 April 2002 |
Stability of microstructure for tetragonal to monoclinic martensitic transformations
1
School of Mathematics, University of Minnesota, 206 Church
Street SE, Minneapolis, MN 55455, USA;
(belik@math.umn.edu)
2
School of Mathematics, University of Minnesota, 206 Church
Street SE, Minneapolis, MN 55455, USA;
(luskin@math.umn.edu)
Received:
29
March
1999
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.