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.