Identification of Simple Shear in Plane Strain Deformation

A theoretical analysis of plane strain incompressible velocity fields is first carried out. Two types of local fields are distinguished according to the sign of $det(L)$⁠, where $L$ is the velocity gradient tensor, whereas $det(L)=0$ is associated with simple shear. A geometrical interpretation is used to illustrate the various decompositions of $L$⁠. Finally, it is suggested that the condition $det(L)=0$ can be used to predict the occurrence of shear bands during metal forming processes.