A nonlinear integral model for describing responses of viscoelastic solids

In this paper we develop a model as well as carry out experiments to test the efficacy of the model, for a class of non-aging isotropic viscoelastic solids. We fashion a nonlinear integral model, which belongs to the class of quasi-linear viscoelastic models, for solid-like materials, which upon linearization reduces to a linear viscoelastic model. The model is defined by separating the normalized time function and nonlinear stress measure that describes the elastic response of the materials. In the case of isotropic materials we consider two independent normalized time functions and two nonlinear stress measures, which are expressed in terms of the stress invariants I1 and I2. We discuss the methodology of the material parameter characterization based on the experimental data available for polyoxymethylene (POM) under quasi-static ramp with constant rate and creep loadings. The response predicted by the nonlinear integral model calibrated by the material parameters obtained through data reduction is then tested against other experimental data under various loading histories. The nonlinear viscoelastic model is capable of capturing the three-dimensional response of POM polymers under various histories of inputs both under stress and strain controlled loadings. Finally we present solutions to boundary value problems (BVPs) of a concentric cylinder made of POM under internal pressure in order to demonstrate one of the applications in which POM is used. The design of structural elements made of POM can be undertaken by using models of the class developed in this work.