Nonlinear Analysis of Rubber-Based Polymeric Materials with Thermal Relaxation Models

ABSTRACT

Using mathematical modeling and computer simulation, nonlinear dynamics of rubber-based polymers has been studied with due regard for the effect of thermal relaxation. Main results have been obtained for the case of elongational oscillations of a ring-shaped body subjected to periodic (“internal”)boundary conditions. Particular emphasis has been placed on high-frequency and short spatial variations of temperature and displacement, in which the role of nonlinearities in the dynamics of the material and their close connection with the effect of thermal relaxation time can be best appreciated. It is shown how the vanishing relaxation time can lead to an attenuation of nonlinear effects in the thermomechanical system.

This research was supported by Australian Research Council Grant 179406. We thank anonymous referees for constructive comments accounted for in the final version of the manuscript.

Notes

¹Recall that in the decomposition of the strain E = E* + 1/3[tr(E)]I, E* is called the distortional part of the strain and tr E is the dilatational part (e.g. [[8]], p. 348).