Research On Numerical Simulations Of Metal Forming Processes By The Adaptive Element-free Galerkin-Finite Element Coupling Method

Metal forming technology plays an important role in the manufacturing industry. It has merits on high productivity, stable quality and effective utilization of raw material. The mechanical performance of the metal is also improved in the forming processes. With the development of numerical methods and IT technology, simulation technology based on the finite element method (FEM) has been widely used in the analysis and prediction of metal forming processes. However, the finite element analysis is based on topological meshes which tend to be distorted in the forming processes. Distorted meshes lead to the deterioration of computational accuracy and even the halt of simulations. As a result, burdensome remeshing procedures have to be implemented. Nevertheless, remeshing remains as a challenging task, particularly for 3D problems. In addition, extra loss of accuracy and efficiency is inevitable.In meshless methods, approximations are constructed in terms of discrete nodes. It is free of the trouble caused by mesh distortion. Meshless methods exhibit their unique advantages in the analysis of bulk metal forming where large deformation takes place frequently. As meshless methods are free of topology, the spatial layout of nodes is flexible. This property endows meshless methods with the capabilities of adaptive analysis. Despite these advantages, the computational efficiency of meshless methods is much lower than that of FEM. This disadvantage restricts their further development and application.In this dissertation, efforts have been made to combine the EFG method with the FEM in the analysis of 2D local bulk metal forming. Based on the coupling methods which have been published, it is intended to implement the dynamic conversion from FEM modeling regions to EFG ones according to the deformation level. An adaptive EFG-FE coupling method based on the rigid-visco plastic flow theory was proposed. Key techniques and algorithms in the numerical analysis were developed.The rigid-visco plastic EFG-FE coupling method for 2D metal forming processes was established. Discretized stiffness matrices and equations are derived according to the mechanics of plasticity and variational theory. The modified penalty function method is used to enforce the incompressible constraints. The boundary singular kernel method is used to impose the essential boundary conditions.Key techniques in the numerical simulation are studied and given in detail. An algorithm is proposed to dynamically determine the sizes of nodal supports, which reflect the node density and local characteristics. The algorithm is effective for both circular supports and rectangular supports. Two schemes are presented to generate background cells and select the order of Gaussian quadrature, respectively, according to the spatial distribution of EFG nodes. Automatic contact treatments are achieved on the dynamic interface between tools and billets.The adaptive EFG-FE coupling method is proposed. It retains both the capability of handling large deformation by meshless methods and high computational efficiency by FEM. During the numerical simulations, FEM elements are converted to EFG nodes automatically according to the level of distortion. Meanwhile, EFG regions are partially reverted to FEM ones according to the strain rate distribution. The schemes to implement adaptive conversion and coupling are elaborated. Numerical examples of local bulk metal forming processes including lateral extrusion, forward extrusion, backward extrusion, forward-backward extrusion and forging were given. The numerical results were compared with the FEM solutions and experimental data. The accuracy and merits of numerical simulations were demonstrated.The formulations for the heat transfer in the metal forming processes were derived. The procedures for thermo-mechanical analysis were given. The thermo-mechanical analysis of axis-symmetric extrusion was implemented.The research in this dissertation shows that the adaptive EFG-FE coupling method makes use of the advantages of both meshless methods and FEM. It is effective for the numerical analysis of local bulk metal forming processes.