UNIQUENESS AND BIFURCATION IN ELASTIC-PLASTIC SOLIDS

The present work is concerned with the problems of uniqueness and bifurcation in a time-independent elastic-plastic material obeying the normality flow rule with a smooth yield surface. Rate n constitutive relations are formulated for the corresponding material. Under selfadjoint boundary conditions, it is shown that every solution of the rate n boundary value problem is governed by a variational principle and the corresponding functional reaches a strict absolute minimum if the solution satisfies a sufficient uniqueness condition. In order to analyse uniqueness and bifurcation, a series of linear comparison solids are constructed. It is shown that Kill's exclusion condition excludes not only rate one bifurcations but also higher order ones.