Plane strain bending under tension of a functionally graded sheet at large strains as an ideal flow process

Abstract

Ideal plastic deformations (ideal flows) have been defined as solenoidal smooth deformations in which an eigenvector field associated everywhere with the greatest (major) principal rate of deformation is fixed in the material. In the case of plane strain deformation of rigid perfectly plastic material obeying an arbitrary isotropic yield criterion and its associated flow rule, it is always possible to find an equilibrium stress field which is compatible with an ideal deformation. It is shown in the present paper that an ideal deformation is possible for functionally graded sheets in the process of plane strain bending under tension. In contrast to the general process, the tensile force and bending moment cannot be prescribed arbitrary but should be found from the solution.