On Uniqueness in Ideally Elastoplastic Problems in Case of Nonassociated Flow Rules

Abstract

It is known that in the quasi-static treatment of ideally elastoplastic solids, lack of uniqueness may occur unless associated flow rules are used. This has been illustrated by a simple example in reference [3]. The present study shows that the uniqueness difficulties in the foregoing and in similar situations disappear, if inertia forces are included in the analysis. As inertia forces in nature are unavoidable there may therefore be nothing improper in the use of nonassociated flow rules. One is simply not permitted to replace the actual dynamic situation in the limit by a quasi-static one. It is shown, however, that an entirely arbitrary selection of yield condition and flow rules is not permissible, but that the combination must satisfy a requirement which is derived. No general proof of uniqueness of dynamic problems for material prescriptions satisfying this requirement is as yet available. It is the purpose of the paper to induce interested investigators to search for such a general proof.