Some mathematical problems in perfect plasticity Original Research Article

Mathematical problems arising in the study of problems of perfect plasticity are reviewed, and some problems of current interest are discussed. In the context of the dual formulation, for which the problem has been thoroughly explored, the strategy of viscoplastic regularization and its application are reconsidered, with a view to exploring the use of this strategy in the study of the primal problem. It is argued that this approach is not without substantial difficulties, and so alternatives to the study of the primal problem are sought. Details are given of an approach by the authors in which direct methods of the calculus of variations are applied to a sequence of time-discrete problems, the solution to the original problem being recovered in the limit as the time step goes to zero.