A non-monotonous damage function to characterize stress-softening effects with permanent set during inflation and deflation of rubber balloons

A non-monotonous stress-softening phenomenological model is applied to study the Mullins effect with residual strains to characterize the inflation and deflation of rubber balloons. It is shown that analytical predictions based on our proposed non-monotonous softening function and the modified stress-softening non-Gaussian average-stretch full-network constitutive equation that accounts for residual strains are consistent with experimental data. Also, we use the constitutive equation for equibiaxial extension to predict stress-softening behavior in a kinematically equivalent simple compression deformation state.