A constructive approach of invariants of behavior laws with respect to an infinite symmetry group – Application to a biological anisotropic hyperelastic material with one fiber family

Anh-Tuan Ta (1) , Frédéric Holweck (1) , Nadia Labed (1) , Alain Thionnet (2) , François Peyraut (1)

1 M3M - Laboratoire Mécatronique 3M - Méthodes, Modèles , Métiers
2 CDM - Centre des Matériaux

In this paper, six new invariants associated with an anisotropic material made of one fiber family are calculated by presenting a systematic constructive and original approach. This approach is based on the development of mathematical techniques from the theory of invariants: • Definition of the material symmetry group. • Definition of the generalized Reynolds Operator. • Calculation of an integrity basis for invariant polynomials. • Comparison between the new (constructed) invariants and the classical ones.

Mots clés: Theory of invariants; Biomechanics; Anisotropic hyperelastic material

Domaines: Science des matériaux [cond-mat.mtrl-sci]

Anh-Tuan Ta, Frédéric Holweck, Nadia Labed, Alain Thionnet, François Peyraut. A constructive approach of invariants of behavior laws with respect to an infinite symmetry group – Application to a biological anisotropic hyperelastic material with one fiber family. International Journal of Solids and Structures, 2014, 51 (21-22), pp.3579-3588. ⟨10.1016/j.ijsolstr.2014.06.019⟩. ⟨hal-01078771⟩