Evaluation of “True stress” for Geometrically Nonlinear Plane Stress/Strain Problems

Abstract

The description of deformation and the measure of strain are essential parts of nonlinear continuum mechanics. In this paper, A new formulation for geometric nonlinear plane stress/strain based on Logarithmic strains (GNLGS) is developed. This is based on the well-known Green's strains and coupled with modifying a formulation based on geometric strains. A geometric nonlinear total lagrangian formulation applied on two-dimensional elasticity using 4-node plane finite elements is used. The formulations are implemented into the finite element program (NUSAP), which is developed for the analysis of plane stress/strain problems subjected to static loading. The solution of nonlinear equations is obtained by the Newton-Raphson method. The program is applied to obtain stresses for the different strain measures. Numerical examples are used to compare the different stresses obtained.