A phenomenological energy-based model to characterize stress-softening effect in elastomers

A phenomenological energy-based model for stress-softening of isotropic, incompressible hyperelastic rubberlike materials is derived here. In this model, the microstructural damage is characterized by an exponential softening function that depends on the current magnitude of the strain-energy function and its maximum previous value in a deformation of the virgin material. Theoretical models are presented for uniaxial, equibiaxial and pure shear deformations by using Gaussian and non-Gaussian material molecular network models. The accuracy of the resulting constitutive equations is demonstrated on uniaxial, equibiaxial and pure shear experimental data provided in the literature. Comparisons between the energy-based model and the strain intensity based phenomenological model described in [Elías-Zúñiga A, Beatty MF. ZAMP 2002;53:794-814. [1]] show that the model developed here is slightly superior in following experimental data.