Pii: S0749-6419(99)00006-6

We study thermomechanical deformations of a viscoplastic body deformed in simple shear. The e€ect of material elasticity is neglected but that of work hardening, strain-rate hardening, thermal softening, and strain-rate gradients is considered. The consideration of strain-rate gradients introduces a material characteristic length into the problem. A homogeneous solution of the governing equations is perturbed at di€erent values t0 of time t, and the growth rate at time t0 of perturbations of di€erent wavelengths is computed. Following Wright and Ockendon's postulate that the wavelength of the dominant instability mode with the maximum growth rate at time t0 determines the minimum spacing between shear bands, the shear band spacing is computed. It is found that for the shear band spacing to be positive, either the thermal conductivity or the material characteristic length must be positive. Approximate analytical expressions for locally adiabatic deformations of dipolar (strain-rate gradientdependent) materials indicate that the shear band spacing is proportional to the square-root of the material charateristic length, and the fourth root of the strain-rate hardening exponent. The shear band spacing increases with an increase in the strain hardening exponent and the thermal conductivity of the material. # 1999 Elsevier Science Ltd. All rights reserved.