Keywords: hyperelasticity, logarithmic strains, Mullins effect, damage mechanics, living tissues, polymers.

Hyperelastic materials are characterized by an energy-preserving behavior which results in an identical path for loading, unloading and reloading. Rubbery materials consist frequently on a cross-linked elastomeric substance containing some percentage of particles of carbon as fillers. Due to such fillers, for example, the virgin loading path differs substantially from the unloading-reloading one. The behavior may then be considered as a result of damage in the material. This effect is known as part of the Mullins effect and is present not only in carbon-filled rubbers but also in biological materials.

In this paper we present a novel formulation of continuum damage mechanics in hyperelastic materials and an efficient computational procedure for modelling the Mullins effect in isochoric, isotropic materials. The formulation is based on the idea that undamaged hyperelastic behavior cannot be measured, but the unloading-reloading behavior of a damaged material can be readily obtained and on that only the unloading-reloading curve presents a real hyperelastic behavior. The unloading-reloading curve may be described by any appropriate constitutive model but using spline-based functions both the virgin loading and the unloading-reloading curves are exactly captured. The model is efficient for finite element implementation.

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