Numerical description of the viscoelastic properties of low- and high-filled elastomeric nanocomposites

In this work, an analytical solution for the change in the dissipative (inelastic) part of the stress tensor at a constant rate of uniaxial loading of the material was obtained within the framework of a new thermodynamic model of the behavior of viscoelastic materials. Uniaxial experiments with nested loading cycles were performed on samples of low- and high-filled elastomeric nanocomposites with different fillers. At the end of each loading and unloading step, time delays were specified to observe the relaxation processes in the material and to experimentally find the equilibrium deformation curve. The obtained equilibrium curve can be described using the elastic potential. Having determined the equilibrium (elastic) and finding the dissipative (inelastic) parts of the stress tensor, we have described the viscoelastic response of the considered elastomeric materials with high accuracy. The graphs of theoretical and experimental curves of deformation of samples of elastomeric nanocomposites are presented. This paper is an expanded version of the work presented at the conference "Mathematics and Interdisciplinary Research 2021" [1].