A visco-hyperelastic constitutive model for rubber-like materials: A rate-dependent relaxation time scheme

A three-dimensional visco-hyperelastic constitutive model is developed to describe the rate-dependent behavior of rubber-like materials at large deformations. The model encompasses a hyperelastic part which uses the “Exp–Ln” strain energy function to characterize the equilibrium response and a viscous part capturing the rate sensitivity using a hereditary integral form which links the overstress to the history of stored strain energy. A physically consistent rate-dependent relaxation time scheme is introduced which reduces the number of required material parameters and also facilitates the calibration process. The proposed model is verified using various uniaxial experimental data in different rate ranges. Furthermore, the model is incorporated via VUMAT in ABAQUS/Explicit to examine its performance in three-dimensional deformations. To this end, finite element analysis of an elastomeric bushing is performed and the results are compared to those of experiment. It is then concluded that, the proposed constitutive relations are quite efficient in predicting the behavior of rubber-like materials in different states of deformation and also in wide ranges of strain rate.