Adaptive finite element computations of shear band formation

We study numerically an instability mechanism for the formation of shear bands at high strain-rate deformations of metals. We use a reformulation of the problem that exploits scaling properties of the model, in conjunction with adaptive finite element methods of any order in the spatial discretization and implicit RungeKutta methods with variable step in time. The numerical schemes are of implicitexplicit type and provide adequate resolution of shear bands up to full development. We find that from the initial stages, shear band formation is already associated with collapse of stress diffusion across the band and that process intensifies as the band fully forms. For fully developed bands, heat conduction plays an important role in the subsequent evolution by causing a delay or even stopping the development of the band.