A nonlinear viscoelastic constitutive model for polymeric solids based on multiple natural configuration theory

In this paper we carry out an experimental study and develop and corroborate a model for describing the response of viscoelastic solids undergoing microstructural changes. We adopt the theory of multiple natural configurations (multi network model) and a single integral constitutive representation to incorporate the effect of microstructural changes on the time-dependent macroscopic deformations of polymers. In formulating the model, we assume that the polymers have two natural configurations, which are different stress-free configurations associated with the original and new networks. The new network is formed when the polymers are subjected to relatively large deformation, leading to the breaking of the junctions in the original network, and is irrecoverable. While the responses of the two networks from their respective natural configuration is elastic, the process of microstructural changes of the original network is dissipative and hence the response of the two networks together is not elastic. Experimental data on polyoxymethylene (POM) under uniaxial tensile quasi-static ramp and creep-recovery histories are used to examine the applicability and efficacy of the model. During testing, deformations in the loading and lateral directions are recorded, which allow for determining various stress-strain measures. We also discuss different mathematical functions that can be considered in describing responses of the polymers based on the recorded stress-strain measures. The model is shown to be capable of describing three dimensional responses of POM polymers under various loading histories.