Explicitly Modeling Stress Softening and Thermal Recovery for Rubber-like Materials

Rubber-like materials exhibit stress softening when subject to loading–unloading cycles, i.e., the Mullins effect. However, this phenomenon can be recovered after annealing the previously stretched sample under a stress-free state. The aim of this paper is to establish a constitutive model with thermodynamic consistency to account for the stress softening and thermal recovery. Towards this goal, (i) an explicit form of Helmholtz free energy can be found such that the restrictions from thermodynamic law can be satisfied; (ii) a compressible, multi-axial strain-energy function considering energy dissipation is proposed by introducing specific invariants; (iii) a unified shape function based on the symmetry property of the test data in a one-dimensional case with stress softening and thermal recovery is provided by introducing a weight variant; (iv) it is proven that the new potential can automatically reduce to the one-dimensional case, i.e., uniaxial tension, equal biaxial, or plane strain; (v) numerical results for model validation are exactly matched with classical experimental data.