A comparison of nonlinear integral-based viscoelastic models through compression tests on filled rubber

Abstract

Carbon black-filled rubber and soft biological tissues are only two examples of materials which undergo large deformation processes and exhibit relevant dissipation and hysteresis losses. Nonlinear viscoelasticity encompass a wide class of constitutive models aimed at describing the behavior of such materials. The main goal of the present paper is to draw a comparison between the many viscoelastic constitutive relations recently proposed. To this aim the current stress value is expressed through a single hereditary integral of the deformation history; this choice, although generalizable, yet permits the introduction of an unifying formulation in which hereditary, strain rate and fractional-derivatives models can all be included. The models comparison is based on several compression tests with cylindrical carbon black-filled rubber specimens carried out at Dipartimento di Ingegneria Chimica e Materiali di Sapienza Università di Roma and in cooperation with the Bridgestone Technical Center Europe SpA. In particular relaxation, creep, loading–unloading cycles at different speeds were considered. For each test case and for each model under consideration, a nonlinear optimization problem is solved to identify the optimal constitutive parameters; the robustness of the identified parameters to perturbations in the experimental data is also computed. The predictive capabilities of the models are then compared in terms of the stress response and the energy dissipation. Finally, the ability of each model in the cross-prediction of the relaxation/creep behavior when identified via cyclic loading and viceversa is examined.