Identification of Simple Shear in Plane Strain Deformation

Abstract

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.