On the spectral constitutive modelling of transversely isotropic soft tissue: Physical invariants

Classical invariants, despite that most of them have an unclear physical interpretation and not having experimental advantages, have been extensively used in modeling nonlinear transversely isotropic soft tissue. In this paper, a new set of spectral invariants that has some advantages over classical invariants, is proposed to model the behaviour of transversely isotropic soft tissue materials. With the aid of the proposed spectral invariant formulation, which is shown to be more general, it is possible to study, in a much simpler manner, the effect of different types of deformations on the response of the material. The proposed strain energy function which contains single variable principal stretch functions is useful in facilitating an experiment to obtain a specific constitutive equation for a particular type of materials. The explicit appearance of the classical ground state constants in the constitutive equation simplifies the calculation for their admissible values. A crude specific constitutive model is proposed for soft tissue and the model fits reasonably well with existing simple shear, biaxial and uniaxial experimental data and managed to predict several sets of experimental data.