Abstract
In the framework of mechanics of plasticity plastic instability has been taken up as the onset of ductile fracture. The occurrence of ductile fracture begins from the appearance of necking phenomena. Hill established a sufficient criterion for uniqueness of boundary-value problem set by given velocities on a part of surface of a body and given nominal traction-rates on the remainder without any restriction placed on changes on geometry. Hill also introduced eigenstates intrinsic to the material wherein the strain can change while the conjugate stress is either stationary or coupled differentially with the strain. The former eigenstate is said to be active, and the latter one is latent. But, identical eigenstate can be obtained under either the latent or the active condition. The latent condition demands work done in second order to vanish, and the active condition corresponds to simultaneous stationary in loads. We adopted the latent condition as the concept of instability, and discussed the onset of plastic instability in several kinds of deformation under hydrostatic pressure. We showed that the eigenstate does not realize simultaneous stationary on loads except for some special cases.
