Research on Natural Element Method and the application to simulate metal forming processes

Abstract

Abstract Due to the special characteristics of metal forming processes (i.e., large deformations, complex nonlinear, etc.), finite element method (FEM) often encounters the mesh distortion problem in simulating large and severe deformation metal forming processes. Once meshes become severely distorted, the whole simulation process cannot be continued unless the remeshing is used. Nevertheless, remeshing usually leads to not only the deterioration of computational precision but also the increase of time-consuming. To solve the problem, a meshless method known as natural element method (NEM) is introduced to analyze metal forming processes in the paper. The shape function of NEM is constructed by employing the natural neighbor interpolation method, and it has the high accuracy of the approximation. In addition, because the shape function possesses the Kronecker δ property like the FEM, the essential boundary conditions can be imposed directly. Therefore, the paper combines NEM with rigid/visco-plastic flow theory and applies it to simulate metal forming processes. Furthermore, a numerical analysis procedure is developed. A numerical example of metal forming processes is analyzed. The validity of the numerical simulation program is evaluated by comparing simulation results with those obtained by rigid/visco-plastic finite element method.