0000000000330770
AUTHOR
Anh-tuan Ta
A new invariant-based method for building biomechanical behavior laws - Application to an anisotropic hyperelastic material with two fiber families
Abstract 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.
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
Abstract 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.