On Simply Laminated Microstructure in Martensitic Crystals
 
                             Bo Li
                    Department of Mathematics
              University of California at Los Angeles
                              and
                    Department of Mathematics
              University of Maryland at College Park
 
                            Abstract
 
One of the most commonly observed microstructure in martensitic
crystals such as metals and alloys is a simply laminated
microstructure.
Such a microstructure can be represented by a sequence of
deformations
whose gradients take values of two compatible constant matrices
on parallel bands with vanishing band size.
 
In this talk, we are concerned with the variational problem of an
elastic energy functional for such a microstructure. To model the
martensitic
phase transformation that leads to microstructure, we assume that
the energy density is rotationally invariant and is minimized on
multiple energy wells. We impose a Dirichlet boundary condition that is
compatible with a simply laminated microstructure.
 
We first show the uniqueness of a simply laminated microstructure
in terms of Young measures generated by gradients of energy minimizing
sequences of deformations. We then present a theory of stability for the
simply laminated microstructure, and discuss its applications to numerical
analysis on the finite element approximations of such a microstructure.
 
This talk summarizes a series of joint works with Mitchell
Luskin, and a recent joint work with Kaushik Bhattacharya 
and Mitchell Luskin.
                         



Request for preprints and reprints address to the speaker at bli@math.ucla.edu
This information can be found at http://www.math.utah.edu/research/