Quasiconformal Hyperelasticity when Cavitation is not Allowed

Tadeusz Iwaniec
Syracuse University

Abstract: My talk features a class of mappings between Euclidean n-domains having finite conformal energy. Using recent topological results I will show that hyperelastic deformations admit a continuous extention to tiny cracks; that is, sets outside which the deformations are injective. The concept of total conformal energy will be introduced. It generalizes the theory of quasiconformal mappings. I will show that the deformations of finite total energy remain injective on the internal cracks of dimension less than $n-1$, establishing the principle of non-penetration of matter. This talk is based on my recent joint work with Jani Onninen.