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

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.