A shear band is assumed to propagate at; a uniform velocity in a thermovisc
oplastic body being deformed in mode-II. The deformation field appears stea
dy to an observer situated on and moving with the shear band tip. The regio
n around the shear band tip is divided into a core region and an inertial r
egion. The core region is behind the shear band tip, and the inertial regio
n surrounds the band tip but excludes a small region around the tip. Asympt
otic fields for the velocity, temperature and the effective stress are dete
rmined in the inertial region. The dependencies of the thermal width of the
band and of the rate of energy dissipated within the core region behind th
e shear band-tip upon the speed of the shear band are exhibited. (C) 1999 E
lsevier Science Ltd. All rights reserved.