Keywords: plasticity, incremental analysis, mixed finite element.

Mixed finite elements are often proposed as elements capable to furnish a high performance response if compared with standard formulations. The mixed formulations are based on the interpolations of the displacement and stress fields and, in the case of elastoplastic structures, a sensible improvement of the element behavior can obtained also through a careful interpolation of the plastic multiplier field inside the element. As also shown in previous works of the authors, this can be a fundamental ingredient of the element formulation.

In order to exploit this richness of the finite element description the nonlinear algorithm used to perform the incremental elastoplastic analysis of the structure requires a suitable appraisal. Standard algorithms are based on strain driven formulations and arc-length solution techniques which evaluate the equilibrium path on the basis of the definition of a sequence of holonomic finite steps in which the constitutive elasto-plastic relationships are integrated usually by using a backward Euler scheme. In this way a nonlinear relationship between assigned increments of displacement and increments of stress and plastic multipliers is included in the generic step, relationships which are exactly solved by using standard return mapping processes. This corresponds to express all the unknowns of the problem as function of the displacements and to reformulate all the problem nonlinearities inside the equilibrium equations. The proposed nonlinear algorithm treats all the unknowns of the problem, displacement, stress and plastic multiplier, as primary variables by retaining all of them at the level of the arc-length iteration. The overall behaviour of the algorithm takes advantage of this approach because of the less nonlinear description of the finite step equations, the procedure is very robust and allows the use of larger step size without detriment to the computational costs.

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