A finite strain framework for the simulation of polymer curing. Part II. Viscoelasticity and shrinkage

A phenomenologically inspired, elastic finite strain framework to simulate the curing of polymers has been developed and discussed in the first part (Hossain et al. in Comput Mech 44(5):621-630, 2009) of this work. The present contribution provides an extension of the previous simulation concept towards the consideration of viscoelastic effects and the phenomenon of curing shrinkage. The proposed approach is particularly independent of the type of the free energy density, i.e. any phenomenologically or micromechanically based viscoelastic polymer model can be utilised. For both cases the same representatives that have been used for the elastic curing models, i.e. the Neo-Hookean model and the 21-chain microsphere model, are reviewed and extended accordingly. The governing equations are derived as well as the corresponding tangent operators necessary for the numerical implementation within the finite element method. Furthermore, we investigate two different approaches-a shrinkage strain function and a multiplicative decomposition of the deformation gradient-to capture the phenomenon of curing shrinkage, i.e. the volume reduction induced by the polymerisation reaction which may lead to significant residual stresses and strains in the fully cured material. Some representative numerical examples conclude this work and prove the capability of our approach to correctly capture inelastic behaviour and shrinkage effects in polymers undergoing curing processes.