Modeling the low-cycle fatigue behavior of visco-hyperelastic elastomeric materials using a new network alteration theory: Application to styrene-butadiene rubber

Although several theories were more or less recently proposed to describe the Mullins effect, i.e. the stress-softening after the first load, the nonlinear equilibrium and non-equilibrium material response as well as the continuous stress-softening during fatigue loading need to be included in the analysis to propose a reliable design of rubber structures. This contribution presents for the first time a network alteration theory, based on physical interpretations of the stress-softening phenomenon, to capture the time-dependent mechanical response of elastomeric materials under fatigue loading, and this until failure. A successful physically based visco-hyperelastic model is revisited by introducing an evolution law for the physical material parameters affected by the network alteration. The general form of the model can be basically represented by two parallel networks: a nonlinear equilibrium response and a time-dependent deviation from equilibrium, in which the network parameters become functions of the damage rate (defined as the ratio of the applied cycle over the applied cycle to failure). The mechanical behavior of styrene-butadiene rubber was experimentally investigated, and the main features of the constitutive response under fatigue loading are highlighted. The experimental results demonstrate that the evolution of the normalized maximum stress only depends on the damage rate endured by the material during the fatigue loading history. The average chain length and the average chain density are then taken as functions of the damage rate in the proposed network alteration theory. The new model is found to adequately capture the important features of the observed stress-strain curves under loading-unloading for a large spectrum of strain and damage levels. The model capabilities to predict variable amplitude tests are critically discussed by comparisons with experiments.     

A multiscale (visco)-hyperelastic modelling for particulate composites

The aim of this work is to pursue, in the wake of the paper [Martin, C., Dragon, A., Trumel, H., 1999. Mechanics Research Communications 26, 327], a non-classical micromechanical study and scale transition for highly filled particulate composites with a viscoelastic matrix. The present extension of a morphologically-based approach due to Christoffersen [Christoffersen, J., 1983. J. Mech. Phys. Solids 31, 55] carried forward to viscoelastic small strain context by Martin et al. [Martin, C., Dragon, A., Trumel, H., 1999. Mechanics Research Communications 26, 327], Nadot-Martin et al. [Nadot-Martin, C., Trumel, H., Dragon, A., 2003. Eur. J. Mech. A/Solids 22, 89], consists in introducing large strain (visco)-hyperelastic behaviour of the constituents (notably the matrix). The form of a local problem is analytically stated for compressive constituents. Numerical simulation for simplified hyperelastic behaviour and regular microstructure, employing different grain/matrix contrast parameters, is discussed in order to illustrate salient features of the advanced approach.