A physically based constitutive model captures the Mullins effect due to different damage mechanisms

Elastomers are widely used in areas such as soft robotics and wearable technology. When subjected to large stretches, elastomers exhibit strain softening behaviors due to damage, commonly known as the Mullins effect. Various damage constitutive models have been developed for this effect, including phenomenological and micromechanical ones. Phenomenological models are simple but lack clear physical explanations, while micromechanical models generally use empirical evolutionary laws tailored to specific damage mechanisms. A simple yet versatile model, applicable to different damage mechanisms, is still lacking. Here, inspired by the extended hyperelastic model, we propose a damage model capable of capturing the Mullins effect due to different damage mechanisms. The model parameters are expressed as a function of a damage factor D. The relation between D and historical maximum stretch is derived from the general minimum energy principle, rather than relying on an assumed empirical function. This approach makes the model adaptable to various damage mechanisms. The Mullins effect was analyzed using this model, under the typical two different damage mechanisms (namely hidden chain stretching and network alteration). Its accuracy is validated through experiments, demonstrating its effectiveness in predicting the Mullins effect with different mechanisms. With only one damage-related parameter, this model offers a feasible approach for capturing the Mullins effect with various damage mechanisms.