The multiscale approach to the curing of polymers incorporating viscous and shrinkage effects

This contribution deals with the modeling of viscoelastic and shrinkage effects accompanying the curing of polymers at multiple length scales. For the modeling of viscous effects, the deformation at the microlevel is decomposed into an elastic and a viscoelastic part, and a corresponding energy density consisting of equilibrium and non-equilibrium parts is proposed. The former is related to the total deformation; it has the form of a convolution integral and depends on the time evolution of the material parameters. The non-equilibrium part depends on the elastic part of deformations only. The material parameters are constant in time, thus an integral form is not necessary. In contrast to the viscous effects, the modeling of shrinkage effects does not require any further extension of the expression for the energy density, but an additional decomposition of the deformation into a shrinkage and a mechanical part. Since the material compressibility is taken into consideration, a multifield formulation is applied for the equilibrium as well as for the non-equilibrium energy part. As a final aspect, the paper includes a study of macroheterogenous polymers for whose modeling the multiscale finite element method is applied. Within this numerical approach, a macroscopic body is treated as a homogeneous body whose effective properties are evaluated on the basis of the simulations which are carried out at the level of the representative volume element. The application of the model proposed is illustrated on the basis of examples studying the influence of individual parameters on the stress state as well as the influence of the volume fraction of different phases at the microscale on the effective material behavior.