Rational Numerical Method for Analyzing Micro Behavior in Macro Deformation.

Abstract

In order to develop a rational numerical method for analyzing micro behavior under macro deformation, the fundamental research to apply the mesh overlay method, known as the s-version FEM, for the metal forming process was achieved in this research. The most important feature of the mesh overlay method is superimposing a fine model, which is called “the local model,” over a part of a whole model, which is called “the global model.” The most important features of the mesh overlay method are (1) the coupled analysis between the global and local models, and (2) the flexibility of mesh discretization. Through this research, the following three facts were newly derived. First, it was concluded that the direct method is suitable for the stiffness equation solver of the mesh overlay method due to its high accuracy. Second, most conventional reports for the mesh overlay method were for linear problems, although most concerns for the metal forming process involve plastic deformation behavior. Therefore, the mesh overlay method was successfully extended to rigid-plastic (nonlinear) problems in this research. The mesh overlay formulations for rigid-plastic deformation problems were newly derived, and numerical examples, including plane strain compression with an inclusion at the center, were shown to verify the derived formulations. Finally, an efficient three-dimensional analysis not only for elastic problem but also for rigid-plastic problem was proposed that couples a two-dimensional global model with a three-dimensional local model by employing the mesh overlay method. Through numerical examples for block compression that includes a spherical inclusion/void at its center, the advantages of the present method were demonstrated.