Shear banding and material instability in finitely deformed compressible materials: An example in thin sheets (Q1206539)

The first part of the paper is a concise review of finite elasto- plasticity of compressible materials. A quasistatic approximation in which inertial terms are neglected is adopted, the incremental equilibrium equations and constitutive relations are given. Two- dimensional field equations corresponding to the case of plane stress in thin sheets are completely provided. These are written as quasilinear partial differential equations in four dependent (components of the tensor of velocity gradient) and two independent variables. The geometric instability of the sheet is connected with the hyperbolicity of the differential equations. Thus the shear bands are associated with the characteristics of quasilinear system. It is found that shear bands might form at angles different from \(45^ \circ\) with respect to principal stress directions.