Evaluation of Engineering Stress for Geometrically Nonlinear Plane Stress/Strain Problems

Abstract

The stress-strain measures are essential parts of nonlinear continuum mechanics. In general structural components or continuum bodies will exhibit large strain when undergoing a geometrically nonlinear deformation process. In this Paper, geometrically nonlinear formulations based on two-dimensional 4-node plane stress and plane strain isoparametric finite elements are developed. The nonlinear formulations are based on the total Lagrangian formulation and using the Green's strains and Geometric strains. The formulations are implemented into a general-purpose nonlinear finite element program NUSAP and the stresses obtained from the two strain measures. Numerical examples are used to compare the 2nd Piola-Kirchoff and the Engineering stresses obtained.