| Numerical simulation technology can describe metal forming process intuitionisticly, make stress analysis of die, and predict defects and failure forms possibly exist in the forming. This technology is a powerful auxiliary means in solving plastic metal forming problems.Meshless numerical methods appeared in 1970's. In these methods, the whole problem domain is discreted by a set of nodes, and iterative meshing and remeshing after mesh distortion in Finite Element method are avoided completely. Besides, they have smooth and high order continuous shape function, which gives them evident advantages in solving metal forming problems with large deformation or local severe deformation.Since Element free Galerkin (EFG) method has a relative mature theoretical basis, and behaves good qualities of high accuracy, rapid convergence, and numerical stability, it is chose in this research. Based on the enrichment work about EFG theory, 2D and 3D rigid plastic and rigid-visco plastic static-implicit meshless codes are developed for the simulation of bulk forming.In this paper, fundamental EFG equations based on nodes are deduced through Moving Least Square (MLS) approximation. The essential quality of smooth and high order continuous of shape function is revealed. Emphatically, parameter-weight distribution curve of three commonly-used weight functions are analyzed. Algorithm of reasonable determining rectangular nodal supports is designed, which instructs the choice of weight function. The approximate precision of MLS technology is evaluated through mathematic function. Also, the foundation of EFG system discrete equations and implementation of integration are illustrated in details. With the developed EFG programs for three representative elastic numerical examples, EFG method realizes the simulation of elastic deformations effectively.In EFG method, since it is difficult to implement integrations of stiffness matrix and nodal force directly, an emphasized effort is made. Firstly, accuracy and effectiveness of three EFG integration schemes are evaluated. Based on the results, Gaussian integration method with background cells is chose. And, a further exploration about the relationship between the integrands and their integration fields is executed, with the resulting conclusion that background cells aligning to nodal supports are the most accurate and effective cells for EFG integrations. Moreover, a module is developed to construct background cells based on rectangular nodal supports inside of problem domain, and auto generating of cells is realized. The correctness of module and validity of integration implementation are validated by several typical numerical examples with irregular nodes and complex boundaries.Rigid plastic and rigid-visco plastic(RP/RVP)material models are used in the EFG simulation of bulk forming process. With the essential boundary condition and volumetric incompressible condition enforced by penalty method, 2D and 3D RP/RVP EFG equations are deduced based on Markov variation principle. The thought and algorithm flow of programming for the EFG static-implicit routine are designed, and the final EFG simulation codes of EFGSMBF are developed in Fortran. Consequently, the EFG simulation of simple forming process is achieved.Concerning complex contact problems, thorough analysis and discussion are made. In this research, the arctangent friction model is chose to compute friction force on contact surfaces, and local coordinate systems are used to implement the skew velocity. With tool surface described by analytical method and mesh discrete method, one time search algorithm and master-slave search algorithm are provided. The normal contact force, normal displacement constraint, and tangent friction force are applied through penalty method. With the realization of contact treatment for complex problems, EFG codes for complicated metal forming process are developed, and their qualities are examined through several examples. This work also motivates the application of RP/RVP EFG method in the metal bulk forming further.
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