Mathematical Approaches to the Study of Smart Materials
Abstract
In this lecture we will describe in an expository fashion several techniques
used to model the behavior of smart materials. The defining characteristic of
these models is as follows: the static deformations that one can observe
minimizes a suitably defined energy in an appropriate class of admissible
deformations. Recently, a significant effort has been made to study the
resulting variational principles (i.e., minimization of non-convex functionals).
We will explain ideas from materials science which underlie the mathematics of
these models and describe some representative results.
