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Beyond polyconvexity: An existence result for a class of quasiconvex hyperelastic materials

: Schneider, Matti


Mathematical Methods in the Applied Sciences 40 (2017), Nr.6, S.2084-2089
ISSN: 0170-4214
ISSN: 1099-1476
Fraunhofer ITWM ()

This 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.