Schneider, MattiMattiSchneider2022-03-052022-03-052017https://publica.fraunhofer.de/handle/publica/24671710.1002/mma.4123This article contains an existence result for a class of quasiconvex stored energy functions satisfying the material non-interpenetrability condition, which primarily obstructs applying classical techniques from the vectorial calculus of variations to nonlinear elasticity. The fundamental concept of reversibility serves as the starting point for a theory of nonlinear elasticity featuring the basic duality inherent to the Eulerian and Lagrangian points of view. Motivated by this concept, split-quasiconvex stored energy functions are shown to exhibit properties, which are very alluding from a mathematical point of view. For instance, any function with finite energy is automatically a Sobolev homeomorphism; existence of minimizers can be readily established and first variation formulae hold.en510journal article