Homogenization of heterogeneous polymers

Conventional homogenization methods are based on the assumption that the material is statistically homogeneous. However, if a material exhibits strain softening behaviour and localization of deformation, this assumption is no longer valid. The obvious solution is to extend the state of the material point with additional statistical moments of the state of the RVE. When long range effects are incorporated into the continuum mechanical description of the material, in the form of supplementary degrees of freedom, these so-called non-local models are capable of describing strain softening. In this paper, a perforated polycarbonate plate is used as a model material. The mechanical behaviour of the RVE will be described by using a compressible Leonov model, which accounts for the time dependent, large strain behaviour, characteristic for solid polymers. At the macroscopic level, non-linear elastic Cosserat mechanics is applied for the equivalent homogeneous material. It is shown to be possible to determine the macroscopic constitutive equations for the equivalent continuum. As application, a tensile test on a single edge notched specimen will be discussed and compared to 'direct simulations'.