Quasiconformal Hyperelasticity when Cavitation is not Allowed
Tadeusz Iwaniec
Syracuse University
tiwaniec@syr.edu
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.