A micromechanically motivated material model for the thermo-viscoelastic material behaviour of rubber-like polymers

The material behaviour of rubber at the micro level is usually described by means of statistical mechanics. In particular, the Neo-Hooke model has been derived in this fashion. The micromechanical modelling can be extended to include also the breaking and reforming of chains. One possible approach at this level is the so-called transient network theory. Using certain assumptions for the chain distributions, one arrives at a continuum mechanical model of finite viscoelasticity which is based on the multiplicative decomposition of the deformation gradient. This means that the inelastic part of the deformation is regarded as an elastic isomorphism. Further, the considerations at the micro level give information about the temperature dependence of the mechanical material parameters. For instance, it can be shown easily that the shear modulus depends approximately linearly on the temperature. This fact has important consequences for thermo-mechanical coupling which have not yet been discussed in detail in the literature.