A finite amplitude wave propagation problem for a pseudo-elastic solid

A constitutive model for an incompressible pseudo-elastic rubberlike solid is proposed. The term pseudo-elastic refers to a solid which has different stress-deformation relations for loading and unloading so that a hysteresis effect is exhibited, and the virgin reference configuration is recovered w hen the solid is unloaded. The model is based on an isotropic hyperelastic strain energy function W(F), where F is the deformation gradient tensor and det[F] = 1, and the stress-deformation relation for loading from an unstre ssed state is the same as that for a hyperelastic solid with strain energy function W(F). Loading (unloading) is assumed to occur when dW(F) > 0 (dW(F ) < 0)and neutral loading when dW(F)= 0. Finite amplitude wave propagation in a semi-infinite pseudo-elastic string, which is subjected to a cycle of tensile loading and unloading at the free end is considered. Numerical results, obtained from an adaptation of the m ethod of characteristics, are presented for a particular form of the propos ed model, which is based on the Mooney-Rivlin strain energy function.