Abstract

Maintaining the topology of objects undergoing deformations is a crucial aspect of elasticity models. Impermeability may be implemented via regularization by a suitable nonlocal functional.

In case of elastic solids whose shape is described by the image of a reference domain under a deformation map, self-interpenetrations can be ruled out by claiming global invertibility. Given a suitable stored energy density, the latter is ensured by the Ciarlet–Nečas condition which, however, is difficult to handle numerically in an efficient way. This motivates approximating the latter by adding a self-repulsive functional which formally corresponds to a suitable Sobolev–Slobodeckiĭ seminorm of the inverse deformation.

This is joint work with Stefan Krömer (Prague).