Improvement of the return mapping algorithm based on the implicit function theorem with application to ductile fracture analysis using the GTN model

Mano, Akihiro ; Imai, Ryuta*; Miyamoto, Yuhei*; Lu, K. ; Katsuyama, Jinya  ; Li, Y. 

Elastic-plastic analyses based on finite element methods are widely applied to simulate the nonlinear behaviors of materials. When the analysis is conducted by an implicit method, the stress values are generally updated with a time increment by using the so-called return mapping algorithm. This algorithm requires solving simultaneous nonlinear equations related to a constitutive model. In the present paper, we proposed a general method to reduce the number of equations in the return mapping algorithm based on the implicit function theorem. In addition, the proposed method was applied to the Gurson-Tvergaard-Needleman (GTN) model that considers the influence of damage due to nucleation and growth of microscopic void in materials in the simulation of the nonlinear behaviors. By using the GTN model with the proposed method, an elastic-plastic analysis was performed by the implicit method for a 4-point bending test of pipe with a through-wall crack. The numerical solution of the variation of the load-load line displacement from the analysis agreed with experimental result. Thus, we concluded that the proposed method is useful for simulating nonlinear behaviors, including void nucleation and growth in materials.