# Stability of microstructure for tetragonal to monoclinic martensitic transformations

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 34, Issue: 3, page 663-685
- ISSN: 0764-583X

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topBelik, Pavel, and Luskin, Mitchell. "Stability of microstructure for tetragonal to monoclinic martensitic transformations." ESAIM: Mathematical Modelling and Numerical Analysis 34.3 (2010): 663-685. <http://eudml.org/doc/197438>.

@article{Belik2010,

abstract = {
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.
},

author = {Belik, Pavel, Luskin, Mitchell},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Martensitic transformation; microstructure; nonconvex
variational problem; simple laminate; tetragonal; monoclinic; volume
fraction; Young measure; finite element; error estimate; stability; uniqueness; simply laminated microstructure; tetragonal to monoclinic martensitic transformations; energy density; rotationally invariant wells; error estimates; finite element approximation},

language = {eng},

month = {3},

number = {3},

pages = {663-685},

publisher = {EDP Sciences},

title = {Stability of microstructure for tetragonal to monoclinic martensitic transformations},

url = {http://eudml.org/doc/197438},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Belik, Pavel

AU - Luskin, Mitchell

TI - Stability of microstructure for tetragonal to monoclinic martensitic transformations

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 3

SP - 663

EP - 685

AB -
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.

LA - eng

KW - Martensitic transformation; microstructure; nonconvex
variational problem; simple laminate; tetragonal; monoclinic; volume
fraction; Young measure; finite element; error estimate; stability; uniqueness; simply laminated microstructure; tetragonal to monoclinic martensitic transformations; energy density; rotationally invariant wells; error estimates; finite element approximation

UR - http://eudml.org/doc/197438

ER -

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