Accurate Numerical Solutions for Elastic-Plastic Models

The accuracy of two integration algorithms is studied for the common engineering condition of a von Mises, isotropic hardening model under plane stress. Errors in stress predictions for given total strain increments are expressed with contour plots of two parameters; an angle in the pi-plane and the difference between the exact and computed yield surface radii. The two methods are the tangent predictor-radial return approach and the elastic predictor-radial corrector algorithm originally developed by Mendelson. The accuracy of a combined tangent predictor-radial corrector algorithm is also investigated. For single-step constant-strain-rate increments the elastic predictor-radial corrector method is generally the most accurate, although errors in angle can be significant. The use of a simple subincrementation formula with any one of the three approaches yields results that would be acceptable for most engineering problems.