Finite viscoelasticity, plasticity and damage of a class of filled elastomers: Constitutive model

A constitutive model is proposed for a class of filled elastomers exhibiting permanent strain at zero stress, in which hyper-visco-elasticity, plasticity and damage are only weakly coupled. The free energy is expressed as the sum of three terms: a hyperelastic term, a positive hardening function, and a negative damage function. The state relations are then established by postulating a dissipation potential and assuming Norton-Hoff type variations of plasticity and damage. An illustrative example of the model potentialities is given, concerning the Mullins' effect.