Hysteresis and time-dependent constitutive modelling of filled vulcanised rubber

Abstract
A constitutive model for the description of the time-dependent behaviour as well as the hysteresis behaviour of filled vulcanised rubber materials is presented. The time dependent behaviour for long-duration loading situations is described by extending Tobolsky's network alteration theory to the large deformation range. In contrast with previous works, the proposed model employs the non-Gaussian network theory as the point of departure. A chain-rupture function and a chain-growth function govern the long-term time-dependent behaviour. The general reaction laws being applied for these functions are applicable for long-duration situations, while possible flexibility changes can appropriately be described. In order to be able to account for the Mullins effect, the time-dependent model is combined with Simo's damage theory. The damage parameter is related to the previous maximum value of the deviatoric part of the Helmholtz free energy. Model parameter characterisation is performed for a modified SI-rubber by means of a true stress controlled measuring method. The constitutive model is implemented into a FEM program, in order to be able to consider rubber products of arbitrary shape and with arbitrary loading situations.