On the problem of simple shear of an incompressible viscoelastic solid under finite deformations

TL;DR

This paper investigates the behavior of an incompressible viscoelastic solid under simple shear with acceleration and stochastic shear rate, revealing normal stresses and stress dispersion dependence on the objective derivative used.

Contribution

It provides an analytical solution for simple shear in viscoelastic solids with a one-parameter Gordon-Schowalter derivative, highlighting effects of acceleration and stochastic shear rate.

Findings

Normal stresses appear under accelerated shear.

Stress dispersion depends on the choice of objective derivative.

Analytical solutions are derived for stochastic shear rate cases.

Abstract

In the framework of a viscoelastic material model, whose constitutive relation is given by a one-parameter family of Gordon-Schowalter derivatives, the problem of simple shear under acceleration and random velocity motion is considered. For motion with acceleration, the presence of non-zero normal stresses is discovered, which corresponds to the Poynting effect previously discovered for this material. A problem in which the shear rate was determined as a linear function of a random variable given from a normal distribution was studied. Within the framework of the methodology proposed by V.A. Lomakin, an analytical solution of the problem is constructed. A significant dependence of the dispersion of the stress tensor components on the choice of the objective derivative was found.