On the determination of constitutive parameters in a hyperelastic model for a soft tissue

The aim of this paper is to study a model of hyperelastic materials and its applications into soft tissue mechanics. In particular, we first determine an unbounded domain of the constitutive parameters of the model making our smooth strain energy function to be polyconvex and hence satisfying the Legendre-Hadamard condition. Thus, physically reasonable material behaviour are described by our model with these parameters and a plently of tissues can be treated. Furthermore, we localize bounded subsets of constitutive parameters in fixed physical and very general bounds and then introduce a family of descrete stress-strain curves. Whence, various classes of tissues are characterized. Our general approach is based on a detailed analytical study of the first Piola-Kirchhoff stress tensor through its dependence on the invariants and on the constitutive parameters. The uniqueness of parameters for one tissue is discussed by introducing the notion of manifold of constitutive parameters, which is locally represented by possibly different physical quantities. The advantage of our study is that we show a possible way to improve of the usual approaches shown in the literature which are mainly based on the minimization of a cost function as the difference between experimental and model results.