A new invariant-based method for building biomechanical behavior laws - Application to an anisotropic hyperelastic material with two fiber families

Anh-Tuan Ta (1) , Nadia Labed (1) , Frédéric Holweck (1) , Alain Thionnet (2, 3) , François Peyraut (1)

1 M3M - Laboratoire Mécatronique 3M - Méthodes, Modèles , Métiers
2 MAT - Centre des Matériaux
3 UB - Université de Bourgogne

In this article, we present a general constructive and original approach that allows us to calculate the invariants associated with an anisotropic hyperelastic material made of two families of collagen fibers. This approach is based on mathematical techniques from the theory of invariants: Definition of the material symmetry group. Analytical calculation of a set of generators using the Noether's theorem. Analytical calculation of an integrity basis. Comparison between the proposed invariants and the classical ones.

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

Domaines: Sciences de l'ingénieur [physics]; Matériaux

Anh-Tuan Ta, Nadia Labed, Frédéric Holweck, Alain Thionnet, François Peyraut. A new invariant-based method for building biomechanical behavior laws - Application to an anisotropic hyperelastic material with two fiber families. International Journal of Solids and Structures, 2013, 50 (14-15), pp.2251-2258. ⟨10.1016/j.ijsolstr.2013.03.033⟩. ⟨hal-00830357⟩