Mathematical foundations of contact interactions in continuum physics
- Akram Sharif (Technische Universität Dresden, Germany)
In continuum physics the underlying laws have to be satisfied not only for an entire body but also for all of its subbodies. Classically these laws account for contact interactions between contiguous subbodies exerted across their common boundary and a well known result by Cauchy constitutes that contact interactions having a continuous density only depend linearly on the normal field of the common boundary. Recent extensions of this theory that also cover the occurrence of certain concentrated contact interactions showed that Cauchy's fundamental result remains true for a suitable collection of sets of finite perimeter as common boundaries of subbodies. But at the same time the classical approach results in a number of problems, among other things, when concentrations occur.
We will present a new approach by Schuricht, which retains the advantages of the classical theory, but at the same time solves some of its problems and allows a more precise description of concentrations and if time permits also sketch possible extensions of this approach. This is joined work with Friedemann Schuricht.