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Construction of polyconvex, anisotropic free‐energy functions
Author(s) -
Schröder J.,
Neff P.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310071
Subject(s) - isotropy , anisotropy , invariant (physics) , mathematics , mathematical analysis , elasticity (physics) , ball (mathematics) , nonlinear elasticity , physics , mathematical physics , nonlinear system , quantum mechanics , thermodynamics
The existence of minimizers of some variational principles in finite elasticity is based on the concept of quasiconvexity, introduced by Morrey [6]. This integral inequality is rather complicated to handle. Thus, the sufficient condition for quasiconvexity, the polyconvexity condition in the sense of Ball [1], is a more important concept for practical applications, see also Ciarlet [4] and Dacorogna [5]. In the case of isotropy there exist some models which satisfy this condition. Furthermore, there does not exist a systematic treatment of anisotropic, polyconvex free‐energies in the literature. In the present work we discuss some aspects of the formulation of polyconvex, anisotropic free‐energy functions in the framework of the invariant formulation of anisotropic constitutive equations and focus on transverse isotropy.

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