A micro-continuum-mechanical material model for failure of rubber-like materials: Application to ageing-induced fracturing

Rubbery polymers are subjected to severe environmental conditions under service. As a consequence of various ageing mechanisms, the outer surface of rubber components hardens in time and cracking occurs as a result of combined mechanical and chemical processes. Conventional phenomenological hyperelastic constitutive models do not account for material softening. Consequently, the stored energy and stresses tend to infinity as stretch increases. In this contribution, a network alteration for the ageing mechanism of rubber-like materials is introduced along with a micromolecular description of material failure. The proposed micro-continuum material model is based on a serial construction of a Langevin-type spring representing the energy storage owing to conformational changes induced by deformation, to a bond potential representing the energy stored in the polymer chain due to the interatomic displacement. For the representation of the micro–macro transition, the non-affine kinematics of the micro-sphere model is used. The Morse potential is utilized for the interatomic bond, which describes the energetic contribution to rubber-like materials and governs the failure of the polymer chain in terms of bond rupture. A novel numerical scheme for the FE implementation of the proposed model is demonstrated. The hardening phenomenon as a result of diffusion limited oxidation of rubber is explained by the principle of mass conservation which dictates simultaneous modulus hardening along with decrease in ultimate stretch observed in aged rubbery polymers.