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A view on anisotropic finite hyperelasticity. (English) Zbl 1026.74013
Summary: The paper presents a modular framework for the formulation of anisotropic hyperelastic materials at large strains. Thereby, additional symmetric second-order tensors are incorporated into free Helmholtz energy density which allow, e.g., the interpretation as structural tensors. In order to prove the analogy between the material setting – usually based on right Cauchy-Green tensor – and the spatial formulation – typically in terms of Finger tensor – we apply the general representation theorem for isotropic tensor functions. As a result, the spatial formats of stress tensors and tangent operators within the anisotropic hyperelastic case are given, whereby a specific additive structure of contributions due to Finger tensor and additional symmetric tensors is obtained.

MSC:
74B20 Nonlinear elasticity
74E10 Anisotropy in solid mechanics
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