The paper presents the theory, model, weak form, finite element method and return-mapping algorithm for the isotropic hardening elastic-plastic problem. Then applying the algorithm to numerically simulate a variety of plane strain problems. | Vietnam Journal of Mechanics, VAST, Vol. 28, No. 2 (2006) , pp. 74 - 82 ABOUT AN APPROXIMATE METHOD TO SOLVE THE STATIC BOUNDARY VALUE PROBLEMS IN THE ISOTROPIC HARDENING ELASTIC-PLASTIC SOLID 1 NGO THANH PHONG , 1 NG UYEN THOI TRUNG , AND 2 NGUYEN PHU VINH 1 University of Natural Sciences, VNU, HCMC, 2 University of Industry, Hochiminh City Abstract. The paper presents the theory, model, weak form , finite element method and return-mapping algorithm for the isotropic hardening elastic-plastic problem. Then applying the algorit hm to numerically simulate a variety of plane strain problems. 1. INTRODUCTION The plasticity theory has been researched in depth in recent decades. The approximate methods to solve the elastic-plastic problems are still topical and challenge researchers. The most difficult problem in elastic-plastic problems is to determine the yield surface which divides the problem domain into the elastic domain and the plastic domain. On the yield surface, the components of stress, strain, displacement have to be continuous. In the elastic domain, we obtain the elliptic equation system with 15 equations and 15 variables. In the plastic domain, with von Mises yield condition, Drucker axiomatics and combined yield law, we obtain the hyperbolic non-linear close equation system. In approximate methods to solve elastic-plastic problems, there are two noticed methods: the variational inequality method by Glowinski , Lions, and Tremolieres [6] , and return-mapping method by Simo and Hughes [3]. In this paper , we use the latter. In the isotropic hardening elastic-plastic model, the elastic range in the stress space is enlarged in both direction of tension and compression when the behavior of the material is in the isotropic hardening phase (, Fig. 2). a a elastic domain in stress spece E. Eo 0~ ~ -cry / IK ~ . • cr cry Fig. 1. The strain - stress relationship in Fig. 2. The elastic range in the stress space isotropic hardening is enlarged
