A new approach to modeling isotropic damage for Mullins effect in hyperelastic materials

Abstract

In this work we present a new approach to damage mechanics in hyperelastic materials and an efficient numerical procedure for modeling the Mullins effect in isochoric, isotropic materials. The formulation is based on the idea that both the virgin loading and the damaged unloading–reloading behavior may be measured, but only the unloading–reloading curve corresponds to hyperelastic behavior. The damaged unloading–reloading curve is the true hyperelastic behavior and may be described by any suitable hyperelastic constitutive model. We employ a spline-based formulation which is known to exactly capture the behavior. The virgin loading curve, which does not correspond to hyperelastic behavior and involves damage evolution is only employed to compute the energy release rate. The procedure does not employ any material parameter (and hence no parameter-fitting procedure) or any explicit damage evolution function. We highlight similarities and differences of the present model with usual damage mechanics models and with pseudo-elasticity. As a result of the detailed computational procedure which simply involves the solution of a nonlinear scalar function, the virgin loading curve and the damaged unloading–reloading curves are exactly captured. The computational algorithm for three-dimensional implicit finite element analysis is also addressed in detail. Examples show that there is no significant increase in computational effort respect to a pure hyperelastic model.