Mathematical Modelling of Bodies with Complicated Bulk and Boundary Behavior

Many recent technological applications, stimulated by the requirements of economy and optimality, call for a revision of the notions of continuum mechanics. Indeed standard, largely folklore, premises of continuum mechanics do not suffice in many situations. Amongst such premises are the concepts of a body modeled by a region with regular boundary, its permanence as an entity determined once for all, the notion of state bearing the deformation (gradient) as the main ingredient, the force system described by a regular pointwise field of stress, pointwise boundary conditions obtained by a formal application of thedivergence theorem, and constitutive equations of simple materials, to mention a few. Multiple scales are often involved.