The time development of eulerian/lagrangian perturbations to simple shear and its applications to shear banding

T of two-dimensional linear disturbances to the simple shear deformation of viscoplastic hardening/softening solids and its consequences on the localization of the plastic flow into shear bands are investigated. Attention is focused on the orientation features of shear banding. A local analysis is carried out on the basis of a generalized Orr-Sommerfeld equation ; the classic time-independent characteristic lines theory is embedded in a time-dependent analysis. It is shown that the characteristic directions are not equivalent when the time evolution is considered, owing to the convective nature of the shear banding instability. The transition between a time-independent behavior for which a pair of shear bands occurs abruptly along the characteristic directions, and a time-dependent regime where a single shear band goes to completion in the shearing direction is discussed.