On the construction of a theory for an ideally plastic body

Abstract

The starting points of a theory for an ideal rigid plastic body are the determination of the limiting surface and of the law of flow. If one may say concerning the latter that it has already been considered in a sufficiently general way different opinions exist concerning the plasticity condition. Ivlev [1] was the first to consider the question of a possible choice of a plasticity condition, employing extremal principles. Upon inverstigating all possible limiting surfaces for the case of an ideal rigid plastic body, Ivlev showed that the Tresca plasticity condition was characterized by minimum work of the stresses for given incremental strains. This circumstance has as a basis the fact that the stress corresponding to the beginning of flow in tension (or an equal value in compression) occurs experimentally at a unique value. Other possible cases for the given initial experimental point were not considered in the above paper, for in the construction of an isotropic theory the choice of the initial point must not have an effect upon the results. It is shown that if any other point is taken as the given initial point, the Tresca plasticity condition loses its extremal property. The first section of this paper considers the question of the choice of a flow condition for the case of given limiting stress in tension, when use is made of two extremal principles. The general case of an arbitrary given point is investigated in the second section.