Extremum theorems and a computational algorithm for an internal variable model of elastoplasticity

We envisage the elastoplastic constitutive relations proposed by J.B. Martin in an internal variable framework. The solutions of the relevant finite-step structural problem are characterized as stationary points of a six-field principle; such a principle is obtained by direct integration of the multi-valued operators which globally collects the field equations and the constitutive relations. A specialization of the six-field principle is shown to yield a minimum principle for displacements and internal variables and a comparison with a minimum principle for the same variables recently proposed in the literature under stronger assumptions is carried out. A minimum principle for displacements and plastic parameters is also derived for the case of piecewise linear yield surfaces. An iterative predictor-corrector algorithm for the numerical solution of the finite-step elastoplastic structural problem is consistently derived from the minimum principle for displacement and internal variables and a sufficient condition for the convergence of the algorithm is provided. The iterative procedure is tested by an illustrative example.