Analysis of the plasticity regions in elastoplastic torsion problem using mixed complementarity algorithm

Resumo

The elastoplastic torsion problem (ETP) consists of defining portions of elasticity and plasticity in the
cross section of a bar twisted by terminal couples. This problem can be modelled by using variational principles
and is considered an obstacle type problem by means of the membrane analogy. At points where the membrane

touches the obstacle, permanent deformations ensues. Thus, the problem can be rewritten as a mixed complemen-
tarity problem and solved using the FDA-MNCP algorithm (Feasible Directions Algorithm for Mixed Nonlinear

Complementarity Problem). In this work, the objective is to analyze the influence of the shape of the cross section
in the resulting regions of plasticity. Some numerical simulations were made for different rectangular proportions,
with the fixed area, to observe how the shape of these regions varies and the percentage they represent in relation
to the total area. In addition, the plastic portions were compared for three sections of the same area and material,
in the formats: disk, square and L.