The modelling of nonlinear rheological behaviour and Mullins effect in High Damping Rubber

High Damping Rubber (HDR) is used in High Damping Rubber Bearings (HDRB) which, in themselves, are dissipating devices in structural systems. The behaviour of HDRB is essentially linked to that of HDR which combines many phenomena such as nonlinearity, time dependence and memory of the loading history, the so called Mullins effect. Mastering the behaviour of bearings implies an accurate understanding of the response of HDR. Consequently, the purpose of this paper is to present a phenomenological material model for a nonlinear rheological mechanical behaviour accounting for Mullins effect of HDR. Many details of its numerical implementation are given. Based on experimental results and literature review, the Distribution of NonLinear Relaxation (DNLR) approach is explored to develop a new numerical model able to simulate nonlinear rheological response of HDR. Modifying the relaxation time regarding von Mises stress is one of the originalities of this model. A relatively simple way of memorising the loading history is implemented in the finite element program Cast3M© to describe the Mullins effect. Experimental tests are simulated. In order to determine model parameters, strategies for parameter identification are proposed. Firstly, parameters of the nonlinear rheological mechanism are optimised by means of relaxation test simulations and monotonic compression tests. Secondly, parameters of the Mullins effect are identified by using simulation of cyclic tensile tests. Finally, comparisons between experimental and numerical results in quasi-static compression and the cyclic shear of HDR are given in order to validate the model.