A visco-hyperelastic damage model for cyclic stress-softening, hysteresis and permanent set in rubber using the network alteration theory

• A network alteration theory for the Mullins effect, the permanent set and the stress-softening.
• Reconciliation between physical and phenomenological approaches.
• Normalized network parameters depend only on the normalized cycle number.

The large deformation time-dependent mechanical response of rubber-like materials under cyclic loading is characterized by stress-softening, hysteresis and permanent set. To describe this set of first-order phenomena a constitutive model integrating the physics of polymer chains and their alteration under cyclic loading is proposed. The time-dependency is considered using a Zener-type framework in which the chain extensibility limit is described with both physical and phenomenological approaches. The efficiency of the proposed constitutive model is illustrated by comparisons with experimental data obtained on a styrene–butadiene rubber submitted to cyclic tension loading up to failure both in constant and variable amplitudes.