Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0981.74042
Bělík, Pavel; Luskin, Mitchell
Stability of microstructure for tetragonal to monoclinic martensitic transformations. (English)
[J] M2AN, Math. Model. Numer. Anal. 34, No.3, 663-685 (2000). ISSN 0764-583X; ISSN 1290-3841/e

Summary: We give an analysis of the stability and uniqueness of a 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 rectangular side, one corresponds to the shearing of square base, and one corresponds to the shearing of the plane orthogonal to a diagonal in square base. We show that a simply laminated microstructure is stable, except for a class of special material parameters. In each case where the microstructure is stable, we derive error estimates for finite element approximation.

MSC 2000:: *74N05 Crystals
74A60 Micromechanical theories
74S05 Finite element methods
49J45 Optimal control problems inv. semicontinuity and convergence
65K10 Optimization techniques (numerical methods)
65N30 Finite numerical methods (BVP of PDE)
74G15 Numerical approximation of solutions

Keywords: stability; uniqueness; simply laminated microstructure; tetragonal to monoclinic martensitic transformations; energy density; rotationally invariant wells; error estimates; finite element approximation

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]