ABSTRACT
Three-dimensional plasticity theory is suitable for orientation of thought, but it is too complicated for practical analyses. Plane stress and axial symmetry are possible simplifications, but a plane strain approach is more useful in geomechanics. In plane strain theory, the stress and velocity subsystems are usually but not always hyperbolic in character and are associated with two distinct families of characteristic curves. A region where the stresses are constant is a region of constant state. Both families of characteristic curves are straight in a region of constant state, and again, the converse is true. If both families of characteristics are straight in a region, then the stresses are constant in the region. The velocity “jumps” across the rigid-plastic boundary. In the rigid region where the strains would be purely elastic but are neglected, velocity is zero everywhere.
