Stress Softening Damage in Strongly Nonlinear Viscoelastic Soft Materials A Physics Informed Data Driven Constitutive Model with Time Temperature Coupling

Abstract

This study presents a novel physics informed, data-driven modeling framework for capturing the strongly nonlinear thermo-viscoelastic behavior of soft materials exhibiting stress softening, with emphasis on the Mullins effect. Unlike previous approaches limited to quasi-static or isothermal conditions, our model unifies rate dependence, temperature sensitivity, large strain cyclic loading, and evolving damage mechanisms. Thermodynamic admissibility is ensured via a custom loss function that embeds the Clausius Duhem inequality and explicitly constrains the damage variable for physically realistic softening. A Temporal Convolutional Network is trained on high fidelity experimental data across multiple temperatures, strain rates, and stretch levels, enabling the model to capture rich thermomechanical coupling and history dependence. The framework generalizes to unseen thermo mechanical conditions, higher strain rates, and larger deformations, and remains robust to input noise. Validation against finite element simulations using Abaqus/Explicit demonstrates excellent agreement under cyclic loading and damage evolution, confirming the surrogate models effectiveness for advanced simulation workflows.