The present paper briefly reviews analytical studies of the evolution of thermo-plastic shear band,i.e.emergence from uniform deformation,post-instability growth and latestage behaviour.The case studied is the simple shear of temperature and rate-dependentmaterials with heat transfer.Uniform mode exists before a critical state,if no heat flows out oftestpiece.Upon reaching the critical state, bifurcation appears as a result of disturbances,which leads to instability and the formation of narrow shear band.Initially,the band,due totemperature disturbance,can shrink with increasing temperature and strain rate owing tounsteady flow.Then heat conduction dominates and causes the shear band to expand.The post-mortem appearance of thermo-plastic shear band manifests itself as balance of plastic work rateand heat diffusion.Melting may also take place within the band.
