A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function

In the present paper we propose a set of orthotropic and transversely isotropic strain energy functions that (a) are polyconvex, (b) are proved to be coercive and (c) satisfy a priori the condition of the stress-free natural state. These conditions ensure the existence of the global minimizer of the total elastic energy and for this reason are very important in the context of a boundary value problem. The proposed hyperelastic model is represented by a power series with an arbitrary number of terms and corresponding material constants which can easily be evaluated from experimental data. For illustration, the model is fitted to uniaxial tension tests of calendered rubber sheets revealing transverse isotropy with respect to the calendering direction. Thus, a very good agreement with the experimental results is achieved. (C) 2004 Elsevier Ltd. All rights reserved.