SOME REMARKS ON PATH INDEPENDENCE IN THE SMALL IN PLASTICITY

Introduction. Drucker's [1] definition of work-hardening has had a significant influence on the development of stress-strain relations in the mathematical theory of plasticity. Also, recognition that this definition provides a condition which is sufficient to ensure uniqueness of solution, in problems involving small deformations, has lead to its consideration as a stability postulate with extensions to time-dependent materials [2, 3] and as a basis for idealized models of soil behavior. The stability postulate assists in defining the class of materials covered by the theory. Some materials are excluded and for these a different starting point must be used. Frictional materials provide a number of examples of exceptions to Drucker's postulate. The postulate also excludes materials that soften. If these are to be brought within the scope of the theory of plasticity, a less restrictive postulate is required which allows softening but still provides the accepted forms of flow rule for hardening plasticity. With this in mind, Drucker has suggested an alternative postulate based on the concept of path independence in the small [4], The object of this paper is to examine some of the implications of this idea. Inviscid plasticity is considered first. Following this, an example of a frictional material is taken to show that the new postulate is restrictive and that some forms of material are excluded. Finally, softening is considered in an application to an ideal material which fractures in a progressive manner.