Polyconvex models for arbitrary anisotropic materials

In: Proceedings in Applied Mathematics and Mechanics, Jg. 8 (2008) ; Nr. 1, S. 10415-10416
ISSN: 1617-7061
Zeitschriftenaufsatz / Fach: Bauwissenschaften
Abstract:
In this work we provide polyconvex models for arbitrary anisotropic materials. The fundamental idea is the introduction of second–order, symmetric and positive definite structural tensors which are motivated by some basic crystallographic geometric relations. The deduced invariant functions automatically satisfy the polyconvexity condition and ensure the requirement of a stress free reference configuration. Restrictions coming along with the polyconvexity condition and the usage of second–order structural tensors will be pointed out. Furthermore the results of three representative fittings show the adaptability of the proposed models for the description of real anisotropic material behavior.

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