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

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.