On a micromechanically-based finite element simulation of the viscoelastic and damage behaviour of rubber-like polymers

Rubber-like polymers are characterized by their ability to undergo extreme elastic deformation. Nevertheless, such materials exhibit noticeable inelastic effects. This is in particular visible, if the stiffness of the polymers is enhanced by filler particles. In order to develop optimal polymer mixtures for industrial use, the incorporation of inelasticity into the material modelling cannot be avoided. Usually this is done at the continuum mechanical level. The disadvantage of such approaches is, however, that a large number of material parameters has to be determined. Due to the non-linearity of the material behaviour, non-linear optimization algorithms have to be applied for this purpose which entails the difficulty that, if a physically reasonable set of material parameters is found, it is probably nor the best neither the unique one. Moreover, the connection to the chemical or physical behaviour of the polymer mixture cannot be directly established, such that it is problematic to draw conclusions in view of a more optimal polymer mixture. For these reasons, a micromechanical approach is much more suitable to develop a polymer “recipe”. In the present paper, we develop a physically-based modelling strategy which uses known information about the molecular structure of polymers, e.g. the number of links of a chain or the number of chains per reference volume. In the work, in particular two inelastic effects are discussed. First of all, we look at the damage behaviour which manifests itself in form of the Mullins’ effect. Secondly, stress relaxation and creep phenomena are investigated. Note that for filled polymers also plastic deformation and friction phenomena have an important influence. However, here, we restrict ourselves to unfilled polymers such that the latter two aspects are not of interest. In unfilled polymers, the inelastic behaviour is controled by the breakage and reformation of chains. These effects can be modelled by using the probability for chain breakage (and reformation) as input for our computational model.