Approximation of a Martensitic Laminate with Varying Volume Fractions

Li, 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 -