On a Damaged Hyperelastic Medium: Mullins Effect with Irreversible Strain

A theoretical model is proposed to describe the damaged hyperelastic behavior of filled rubber-like solids. Special emphasis is laid on two specific phenomena: the Mullins effect (i.e., strain induced stress softening) and irreversible (i.e., permanent) strain. Often observed in the behavior of the hyperelastic rubber-like materials, these two phenomena are supposed to be exclusively induced (and then governed) by isotropic damage (cavities and holes) initiation and growth. Using the classical Continuum Damage Mechanics (CDM) together with the generalized normality rule, a constitutive model is proposed to account for these two effects of damage. After a choice of constitutive functions, the obtained model is applied to four different loading paths classically studied in the case of this type of filled elastomeric material.