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Beyond polyconvexity: an existence result for a class of quasiconvex hyperelastic materials
Author(s) -
Schneider Matti
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4123
Subject(s) - quasiconvex function , hyperelastic material , mathematics , nonlinear system , sobolev space , mathematical analysis , nonlinear elasticity , class (philosophy) , calculus of variations , elasticity (physics) , pure mathematics , calculus (dental) , geometry , convex analysis , computer science , medicine , physics , dentistry , convex optimization , quantum mechanics , regular polygon , artificial intelligence , materials science , composite material
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. Copyright © 2016 John Wiley & Sons, Ltd.