Axial–Torsional Path Dependence in an Elastoplastic Rod with a Multiply Connected Cross-Section

Abstract

This paper addresses the elastoplastic torsion and tension of a prismatic bar with a multiply connected circular cross-section containing one central and four symmetrically arranged lateral holes. The relevance of this problem stems from the fact that internal contours alter the shear-stress flow, amplify local gradients, and cause non-uniform development of plastic zones. The study considers a two-parameter loading scenario. It is demonstrated that for the same final combination of axial force and torque under different strain trajectories, the equivalent-stress fields and effective torsional stiffness significantly depend on the loading sequence. The obtained results confirm the necessity of simultaneously considering hole geometry, plastic flow, and loading history when analyzing multiply connected bars.