A phenomenological model for healing and hysteresis in rubber-like materials

We propose a predictive model for the dissipative behaviour of rubber-like materials. In the spirit of De Tommasi et al. [D. De Tommasi, G. Puglisi, G. Saccomandi, A micromechanics based model for the Mullins effect, J. Rheol. 50 (2006) 495–512], we assume that at the scale of the polymeric network the material is constituted by a distribution of links with variable activation and fracture thresholds. By considering the recross-linking effect due to unloading we obtain a three-dimensional, non-linear damage model that describes the rate-independent hysteretic behaviour observed in rubber-like solids. The feasibility of the model in treating complex non-homogeneous deformation histories is shown through a numerical application.