A tangent-secant approach to rate-independent elastoplasticity: formulations and computational issues

A general and robust solution procedure for nonlinear finite element equations in small strain elastoplastic structural problems is presented. Its peculiar feature lies in the choice of the most suitable constitutive operator to be adopted at each iteration of a generic load step in order to ensure the utmost stability and convergence rate. Namely, the consistent tangent operator is replaced by a secant one, or vice versa, whether the adopted norm of the residual does not, or does, conveniently decrease at the current iteration. The secant operator is defined as to recover the finite-step increment of the plastically admissible stress from the total, not iterative, strain increment. The original formulation of the solution procedure, consisting of alternate tangent and secant iterations, is then extended to achieve an effective coupling with line searches. The excellent performances of the two procedures are illustrated by numerical examples carried out for typical benchmark problems in plane strain and three-dimensional cases.