# Approximation of a Martensitic Laminate with Varying Volume Fractions

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 1, page 67-87
- ISSN: 0764-583X

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topLi, Bo, and Luskin, Mitchell. "Approximation of a Martensitic Laminate with Varying Volume Fractions." ESAIM: Mathematical Modelling and Numerical Analysis 33.1 (2010): 67-87. <http://eudml.org/doc/197460>.

@article{Li2010,

abstract = {
We give results for the approximation of a laminate with
varying volume fractions for multi-well energy minimization
problems modeling martensitic crystals that
can undergo either an orthorhombic
to monoclinic or a cubic to tetragonal transformation.
We construct energy minimizing sequences of deformations which satisfy
the corresponding boundary condition, and we
establish a series of error bounds in terms of the elastic energy
for the approximation of the limiting macroscopic
deformation and the simply laminated microstructure.
Finally, we give results for the corresponding finite element
approximation of the laminate with varying volume fractions.
},

author = {Li, Bo, Luskin, Mitchell},

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

keywords = {martensitic transformation; simple laminate;
volume fraction; Young measure; finite element; error estimate; orthorhombic to monoclinic transformation; multi-well energy minimization; martensitic crystals; cubic to tetragonal transformation; energy minimizing sequences; error bounds; finite element approximation},

language = {eng},

month = {3},

number = {1},

pages = {67-87},

publisher = {EDP Sciences},

title = {Approximation of a Martensitic Laminate with Varying Volume Fractions},

url = {http://eudml.org/doc/197460},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Li, Bo

AU - Luskin, Mitchell

TI - Approximation of a Martensitic Laminate with Varying Volume Fractions

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 1

SP - 67

EP - 87

AB -
We give results for the approximation of a laminate with
varying volume fractions for multi-well energy minimization
problems modeling martensitic crystals that
can undergo either an orthorhombic
to monoclinic or a cubic to tetragonal transformation.
We construct energy minimizing sequences of deformations which satisfy
the corresponding boundary condition, and we
establish a series of error bounds in terms of the elastic energy
for the approximation of the limiting macroscopic
deformation and the simply laminated microstructure.
Finally, we give results for the corresponding finite element
approximation of the laminate with varying volume fractions.

LA - eng

KW - martensitic transformation; simple laminate;
volume fraction; Young measure; finite element; error estimate; orthorhombic to monoclinic transformation; multi-well energy minimization; martensitic crystals; cubic to tetragonal transformation; energy minimizing sequences; error bounds; finite element approximation

UR - http://eudml.org/doc/197460

ER -

## Citations in EuDML Documents

top- Andreas Prohl, An adaptive finite element method for solving a double well problem describing crystalline microstructure
- Pavel Bělík, Mitchell Luskin, Stability of microstructure for tetragonal to monoclinic martensitic transformations
- Pavel Belik, Mitchell Luskin, Stability of microstructure for tetragonal to monoclinic martensitic transformations
- Pavel Bělík, Timothy Brule, Mitchell Luskin, On the numerical modeling of deformations of pressurized martensitic thin films
- Pavel Bělík, Timothy Brule, Mitchell Luskin, On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films

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