Extension of the Sussman–Bathe spline-based hyperelastic model to incompressible transversely isotropic materials

In this paper we extend the Sussman–Bathe spline-based hyperelastic isotropic model to predict the behavior of transversely isotropic isochoric materials. The model is based on an uncoupled decomposition of the stored energy function and a generalization of the inversion formula used by Sussman and Bathe. The present extension introduces some approximations that, in all studied cases, do not yield relevant deviations from the experimental data. The isotropic model results in a particular case of the present formulation. Several possibilities of user-prescribed experimental data are addressed. The model is used to predict experiments of calendered rubber and of biological tissues.

► We extend the Sussman–Bathe hyperelastic formulation to transversely isotropic materials using a new inversion formula. ► An uncoupled decomposition of the stored energy function in terms of logarithmic strains is proposed. ► Several cases of possible available test data to define the model are carefully addressed. ► It is shown that the model recovers the Sussman–Bathe formulation for the isotropic case. ► The model prediction capabilities for calendered rubber and biological tissues are shown.