A new modelling of the Mullins'effect and viscoelasticity of elastomers based on physical approach

The mechanical behaviour of elastomers is known to be highly non-linear, time-dependent and to exhibit hysteresis and stress-softening known as the Mullins effect (Mullins, 1948) upon cyclic loading. These phenomena are classically studied and modelled independently. Some studies are based on physical approaches (Arruda and Boyce, 1993; Bergström and Boyce, 1998; Marckmann et al., 2002) in which macroscopic constitutive equations are build in regards with the physics of polymeric chains. In this context of physical considerations, the aim of the present paper is to study independently each phenomenon involved in rubber-like materials and to assemble them in a global constitutive equation. First, the hyperelastic behaviour of elastomers is modelled by the physical approach of Arruda and Boyce (1993), widely known as the eight-chains model. This model accurately reproduces the large strains elastic behaviour of elastomers under different types of deformation. Second, the hysteretic time dependent behaviour is approached by the model developed by Bergström and Boyce (1998) that considers the separation of the network in two phases: an elastic equilibrium network and a viscoelastic network that captures the nonlinear rate-dependent deviation from equilibrium. This model is quite simple and successfully reproduces the rate-dependent hysteretic properties of elastomers. Last, as shown in the bibliography, the Mullins stress-softening effect can be considered as a damage phenomenon which only depends on the maximum stretch attained during the deformation history (Govindgee and Simo, 1992). In the present approach, the physical theory of Marckmann et al. (2002) based on an alteration of the polymeric network is adopted. This theory was introduced in the eight-chains hyperelastic model and successfully simulates the decrease of the material stiffness between the first and the second loading curves under cyclic loading. As these three models are based on the physics of the polymeric network, they are gathered in a new efficient constitutive equation. This model is able to reproduces imultaneously the Mullins effect and the time-dependent hysteretic behaviour of elastomers. Finally, the constitutive parameters of this new model are identified by fitting experimental data