Spontaneous dissipation of elastic energy by self-localizing thermal runaway

TL;DR

This paper models thermal runaway in viscoelastic solids, showing how localized heating and strain lead to shear banding, with analytical and numerical methods revealing key parameters controlling instability.

Contribution

It introduces a continuum model with Arrhenius viscosity dependence, analytically and numerically analyzing thermal runaway and shear band formation in viscoelastic materials.

Findings

Thermal runaway onset depends on two key dimensionless parameters.

Runaway leads to extreme spatial localization of strain and temperature.

A simple relation links shear stress, displacement, shear-band width, and temperature rise.

Abstract

Thermal runaway instability induced by material softening due to shear heating represents a potential mechanism for mechanical failure of viscoelastic solids. In this work we present a model based on a continuum formulation of a viscoelastic material with Arrhenius dependence of viscosity on temperature, and investigate the behavior of the thermal runaway phenomenon by analytical and numerical methods. Approximate analytical descriptions of the problem reveal that onset of thermal runaway instability is controlled by only two dimensionless combinations of physical parameters. Numerical simulations of the model independently verify these analytical results and allow a quantitative examination of the complete time evolutions of the shear stress and the spatial distributions of temperature and displacement during runaway instability. Thus we find that thermal runaway processes may well develop under nonadiabatic conditions. Moreover, nonadiabaticity of the unstable runaway mode leads to continuous and extreme localization of the strain and temperature profiles in space, demonstrating that the thermal runaway process can cause shear banding. Examples of time evolutions of the spatial distribution of the shear displacement between the interior of the shear band and the essentially nondeforming material outside are presented. Finally, a simple relation between evolution of shear stress, displacement, shear-band width and temperature rise during runaway instability is given.