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

Vladislav V. Kozhukhov

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arXiv · 2512.19708

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

Vladislav V. Kozhukhov

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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.

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Vladislav V. Kozhukhov. 2025-12-14. On the problem of simple shear of an incompressible viscoelastic solid under finite deformations. https://arxiv.org/abs/2512.19708

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