Extending the theory of pseudo-elasticity to capture the permanent set and the induced anisotropy in the Mullins effect

A new modelling framework is proposed to predict the inelastic features in elastomers' mechanical behaviour such as the Mullins effect, the permanent set and the induced anisotropy. While based on the pseudo-elasticity theory, our model departs from the classical theory on three counts: (i) a separable damage parameter Omega, separable in the principal stretches, is devised and incorporated to facilitate capturing the induced anisotropy; (ii) the damage variable is directly incorporated into the hyperelastic strain energy function to capture the permanent set, and (iii) a specific functional form for the damage parameter is considered, conducive to modelling the foregoing behaviours. The devised framework is then specialised using a recently proposed strain energy function W and is validated against various experimental datasets ranging from filled natural and silicon rubbers, to synthetic rubbers and hydrogels. It is shown that the proposed model favourably captures the inelastic behaviours of interest exhibited by the specimens, and the devised modelling framework facilitates obtaining those favourable fits via a reduced number of model parameters compared with the existing theories in the literature. The proposed framework may also be used directly in conjunction with other strain energy functions for a versatile modelling of the Mullins effect in the finite deformation of rubber-like materials