Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening.

For a class of elastic-plastic constitutive laws with nonlinear kinematic and isotropic hardening, the problem of determining the response to a finite load-step is formulated according to an implicit, backward-difference (stepwise-holonomic) scheme for time integration, with reference to discrete structural models. This problem is shown to be amenable to a nonlinear mathematical programming problem and a criterion is derived which guarantees monotonic convergence of an iterative predictor-corrector algorithm for the solution of the finite-step analysis problem. A version of this algorithm apt to both speed up and guarantee convergence is tested by an illustrative example.