PLANE-STRESS LINEAR HARDENING PLASTICITY THEORY

The accuracies of plane stress integration algorithms for a Goel and M alvern (J. Appl. Mech. 37 (1970) 1100-1106) model for isotropic/kinema tic linear hardening plasticity are studied using error maps. The erro r maps are found to be in agreement with a previous study by Whirley e t al. (Eng. Comput. 6(2) (1989) 116-126) but half of each map was omit ted in that study. Most conventional integration methods use the radia l return method to solve the plasticity equations and iteratively sati sfy the plane strain constraint almost exactly so that all methods giv e the same error maps. Four initial stress cases are considered, equal ly spaced around the VonMises yield surface in the pi-plane. For all t hese presently used methods, the errors are highest for the case of no hardening, with stress errors as large as 38%. A new set of different ial equations similar to the Krieg and Krieg (J. Pressure Vessel Techn ol. 99 (1977) 510-515) equations are developed for the kinematic and i sotropic hardening model and these are reduced to a single ordinary sc alar integral. A new integration method is also developed based on the new equation. This method is found to have a maximum error of only 12 %. It uses a truncated iteration method to satisfy the plane stress co nstraint, but uses an initial estimate for the out-of-plane strain as well as a drag stress which is developed from the radial return method . A second solution is found with an average between that and a consta nt volume value, and the third out-of-plane strain increment is found using a Newton method. Error maps and an example problem are presented and the various methods are compared to an ''exact'' constitutive mod el. The stress errors from the common iterative plane stress method ar e shown to be as high as 20% on this engineering problem, about three times the error of the new plane stress algorithm. (C) 1997 Elsevier S cience B.V.