Regulating cyclic behaviors of tough soft materials: A generic, mechanism-based damage model approach

Tough soft materials like elastomers and tough hydrogels, exhibit complex cyclic behaviors (e.g., Mullins effect, residual stretch, induced anisotropy), which are critical for material toughness and service reliability. In material synthesis, crosslinking agents and filler particles regulate polymer network architecture to influence cyclic responses, yet experimentally parameter optimization is inefficient. Developing a theoretical framework to quantitatively link microscale synthesis parameters with macroscale cyclic behaviors is essential for rational material design. This study proposes a generic, mechanism-based damage model with thermodynamical consistency to address this challenge. Incorporating micro-damage mechanisms (crosslink breakage, chain scission, and entanglement degradation) and integrating a refined single-chain model with a polydisperse micro-sphere network, the model uses a single damage internal variable (active chain density) to quantify damage effects. Through a novel integration of graph theory, a direct correlation is established between model parameters and crosslinker concentration, enabling translation of synthesis inputs into predictable cyclic responses. The damage model is capable of quantitatively capturing multiaxial cyclic behaviors, residual stretch, and induced anisotropy across materials (e.g., rubbers, double-network hydrogels, triple-network elastomers, nanocomposite hydrogels), and can be applied to regulate cyclic behaviors via crosslinker concentration optimization and reveal micro-damage pathways. This work bridges the microscale-macroscale gap in soft material design, offering a robust theoretical tool for optimizing cyclic performance while uncovering fundamental damage mechanisms in tough polymeric materials.