Disturbed Boundary Condition in Analyses of Shear Banding

Abstract

Hill and Hutchinson [J. Mech. Phys. Solids, 23, 239-264 (1975)]studied shear-band bifurcation which is investigated for an incompressible rectangular block constrained to undergo plane deformation. The block is assumed to be made of an incrementally-linear solid. Continuing equilibrium between both side regions separated by a shear plane gives a mode equation which is derived from the condition for the indefiniteness of velocity gradients. On the other hand, Needleman[J. Mech. Phys. Solids, 27, 231-254 (1979)]deduced the same equation based on maintaining equilibrium between these side regions in place of continuing equilibrium. However, in the process of obtaining the mode equation it is ignored in these analyses that these side regions must be under identical boundary condition. Then, this paper examines using Hencky constitutive equations whether the necessity of identical boundary condition is satisfied or not. Consequently, it is found that maintaining of identical boundary condition is disturbed. Hence, no reliance is made on the information in shear banding obtained according to these analyses.