A new hyperelastic model for transversely isotropic solids

Abstract.

Experimental studies on porous materials show a clear dependence of the elastic parameters on the state of stress. In this paper, the implications of this stress dependency on the recoverability of strain and on the work done during a closed stress path for transversely isotropic materials are examined. The necessary and sufficient conditions for an elastic material to be hyperelastic are given. It is shown that the elastic parameters cannot depend on the third stress invariant and that the shear modulus in the plane normal to the axis of symmetry is a linear combination of the other parameters (i.e. the Saint-Venant's approximation [1] is satisfied). Finally, an example of application of the proposed hyperelastic model is presented.