Computational modelling for description of rubber-like materials with permanent deformation under cyclic loading

When carbon-filled rubber specimens are subjected to cyclic loading, they do not return to their initial state after loading and subsequent unloading, but exhibit a residual strain or permanent deformation. We propose a specific form of the pseudo-elastic energy function to represent cyclic loading for incompressible, isotropic materials with stress softening and residual strain. The essence of the pseudo-elasticity theory is that material behaviour in the primary loading path is described by a common elastic strain energy function, and in unloading, reloading or secondary unloading paths by a different strain energy function. The switch between strain energy functions is controlled by the incorporation of a damage variable into the strain energy function. An extra term is added to describe the permanent deformation. The finite element implementation of the proposed model is presented in this paper. All parameters in the proposed model and elastic law can be easily estimated based on experimental data. The numerical analyses show that the results are in good agreement with experimental data.