We intend to address the need for a fundamental understanding of the physical
origin, the mathematical behavior, and the numerical treatment of models
which include microstructure. We shall pursue this aim by a joint effort
involving mathematical analysis, numerical
analysis, computational mechanics, material modelling and experiment.
The mathematical analysis will be based on methods from the
calculus of variations, while in the numerical implementation global
optimization algorithms will play a central role. The
modeling will cover all length scales, from the atomic structure up to
macroscopic samples. The development of the models will be guided by
experiments on single and polycrystals, and results will be checked
against experimental data.