A linearization solution for elastic-plastic torsion problems by Edge-based smoothed finite element method

Abstract

This paper proposes a new scheme for calculating the elastic-plastic uniform torsion of rods considering the hardening behavior of the material. Using PRANDTL-REUSS equation under Hencky proportional loading condition, we develop an elastic-plastic torsion governing equation that can be applied to materials with arbitrary multilinear hardening forms. The edge-based smoothed finite element method is applied to solve the boundary value problem of the above equation. In addition, the incremental scheme is used to calculate the plastic torque. Using the Lagrange interpolation method, the Mises stress is calculated by calculating the gradient in the cell. The nodal stresses are obtained by averaging the stresses at the centroid of the cells. After each load step, the overall domain is divided into elastic and plastic zones according to the yield stresses of the material, and then different governing equations are applied in the different zones. To summarize, this paper provides linearization solutions for nonlinear torsion.