On the solutions of elastic-plastic problems with contact-type boundary conditions for solids with loss-of-strength zones

A formulation of a quasi-static problem of the mechanics of elastic-plastic bodies with loss-of-strength zones and boundary conditions of contact type is given which enables the properties of the loading system to be taken into account. With certain constraints on the constitutive relations and using a condition for stability of the softening process in a local zone, theorems are proved on the uniqueness of the solution of the boundary-value problem and on the maximum and minimum of the functionals when the kinematically or statically possible and actual fields are the same. The corresponding generalized variational principles are given. (C) 1998 Elsevier Science Ltd. All rights reserved.