Plane Strain Slip Line Theory for Anisotropic Rigid/plastic Materials

A SLIP line theory governing states of incipient plane flow at the yield point load is developed for anisotropic rigid/plastic materials which exhibit a reduced yield criterion, governing states of plane flow, that depends only on the deviatoric parts of the in-plane stress tensor. It is shown that every homogeneous, incompressible material which complies with the principle of maximum plastic work, but which is of otherwise arbitrary anisotropy, is of this class. The stress equilibrium requirements are seen to take a remarkably simple form expressing the constancy of the quantities mean in-plune normal stress plus or minus arc length around the governing yield contour in a Mohr stress plane along members of the two slip line families. Further, this generalization of the Hencky equations is valid for every material of the considered class. Some special features of yield contours containing comers and flat segments are discussed, and velocity equations are given for materials complying with the maximum work inequality. The theory is applied to obtain the solution for indentation of an arbitrarily anisotropic half-space with a flat-ended, rigid, frictionless punch. A simple, universal formula, involving only geometrical dimensions of the governing yield contour, is derived for the yield point indentation pressure.