Temporal evolution of shear band thickness

Boundary layer methods are used to derive expressions for the jump discontinuities in velocity, stress gradient and temperature gradient across a shear band. This analysis also yields an expression for the temporal evolution of the thermal boundary layer width, which can be interpreted as a measure of shear band thickness. The jump discontinuities are used to formulate a simplified version of the boundary value problem for the half-slab geometry. Calculated results for an illustrative example reveal a shear band thickness which evolves by initially narrowing and then later widening as diffusion becomes significant.