A finite strain visco-hyperelastic damage model for rubber-like materials: theory and numerical implementation

Many rubber-like materials exhibit hyperelastic, time-dependent, rate-dependent and progressive damage behaviors. In our previous work (Lu et al., 2020), we proposed a hyperelastic damage model to characterize the strain-softening behavior of soft materials. The model modifies the strain energy function of a single chain by introducing an internal damage variable D and then maps the deformation of chains to the macroscopic deformation. In this work, we extend this model to incorporate the time-dependent viscous effect using the Prony series-based nonlinear theory. We further implement the finite strain visco-hyperelastic damage model into finite element software ABAQUS by a user material subroutine UMAT. We use the experimental data of a kind of acrylic polymer under uniaxial tension in literature to calibrate the model parameters, including 4 time-independent parameters and 6 time-dependent parameters. We then use the calibrated parameters to simulate the uniaxial tension and stress relaxation of the acrylic polymer specimen with a complex geometry. The simulated results agree with the experimental data with a remarkable accuracy.