  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.
