Study On The Numerical Simulation Of Bulk Forming Processes By Reproducing Kernel Particle Method

With the development of computer technology and numerical analysis, rigid-plastic finite element method (FEM) has been widely applied in the simulation of bulk metal forming. However, FEM presents some limitations in handling large plastic deformations because the mesh becomes severely distorted. In order to simulate the whole forming process, remeshing is required. Remeshing not only increases computational efforts significantly, it also reduces the overall accuracy of the results. Particularly, reliable and high-quality 3D meshing and remeshing techniques in metal forming are still difficult to achieve, which has become a bottleneck restricting the further development of 3D FEM simulation. Meshless (or meshfree) methods are a new type of numerical methods developed in 1990s. In meshless methods, a continuum body is discretized by a finite number of particles (or nodes) and the displacement field is interpolated under these particles without the aid of an explicit mesh. This characteristic can eliminate mesh distortion which is unavoidable in FEM. As one of the most important meshless methods, reproducing kernel particle method (RKPM) not only has the features of general meshless methods, it also possesses many other advantages. Therefore, RKPM has been widely studied by researchers all over the world.The research on the numerical simulation of 2D and 3D bulk forming processes by the reproducing kernel particle method (RKPM) is carried out in the dissertation. The classical incompressible rigid-(visco)plastic material model is employed. The basic theory, key treatment techniques, and simulation systems are developed in order to further expand the application of RKPM in metal forming and promote the generalization, automation and practicality of meshless simulation in bulk forming. The main work and innovations are:(1) The 2D rigid-(visco)plastic reproducing kernel particle method is proposed by combining RKPM with the flow theory of 2D rigid-(visco)plastic mechanics. The velocity field is constructed by the reproducing kernel approximations. For the treatments of essential boundary conditions and incompressibility constraint, the boundary singular kernel method and the modified penalty method are utilized, respectively. The arc-tangential friction model is employed to treat the contact conditions. According to the incomplete generalized variational principle for rigid-(visco)plastic material model, the stiffness equation for the analysis of 2D bulk metal forming using RKPM is derived. The meshless numerical simulation of 2D bulk forming by RKPM is realized.(2) The key techniques for the realization of generalization and automation in the 2D rigid-(visco)plastic reproducing kernel particle method are studied. The integration process is accomplished by using the rectangular background cell. The rectangular influence domain and tensor product weight function are used. The nonlinear system equation is solved by establishing the initial velocity of the iterative procedure through the direct iteration method. Arbitrarily shaped dies are described by lines and arcs and the technique for automatic treatment of contact boundaries is introduced into meshless method. The modified penalty method is proposed to treat the incompressibility constraint and prevent possible numerical errors resulting from volumetric locking in the rigid-plastic meshless method. Moreover, it is proved theoretically that the modified penalty method is identical to volumetric strain rate projection method when the volumetric strain rate is projected onto constant field. The modified penalty can effectively treat the volumetric locking including the most severe over-constrained condition and prevent the occurrence of pressure oscillation.An adaptive approach for determining the size of influence domain is proposed based on the background integration cell. The advantages of the proposed approach are: the size of influence domain can be adjusted adaptively according to the density of nodes; for the linear basis function, the number of nodes in influence domain for field approximation is chosen to be around 4~8, which assures that adequate nodes are included in influence domain; the new approach is based on the local research algorithm instead of the whole problem domain, thus the calculation efficiency can be greatly improved.(3) On the basis of the work in 2D problems, the 3D rigid-(visco)plastic reproducing kernel particle method (RKPM) is proposed by combining RKPM with the flow theory of 3D rigid-(visco)plastic mechanics. The key techniques for the realization of generalization and automation in 3D numerical simulation of metal forming processes by RKPM are studied. The integration process is accomplished by using the hexahedral background cell. The brick influence domain and 3D tensor product weight function are used. For the 3D linear basis function, the number of nodes in influence domain for field approximation is chosen to be around 8~12. Arbitrarily-shaped 3D die surfaces are represented by small triangular elements. A 3D nonlinear contact treatment algorithm is given and the meshless analysis of unsteady 3D bulk forming with arbitrarily-shaped dies is realized.(4) Meshless simulation systems for 2D and 3D bulk forming processes, 2D-MForming (2D Meshless Forming), 3D-MForming (3D Meshless Forming), have been developed. The typical 2D bulk forming processes including plane-strain upsetting, axisymmetric upsetting, ring compression, plane-strain extrusion and the typical 3D bulk forming processes including upsetting, forging, back extrusion, compound extrusion are analysed. The numerical results are compared with those obtained by rigid-plastic FEM and experimental data. The effectiveness of the proposed theories and key techniques in the dissertation is justified.(5) The low calculation efficiency in meshless method, particularly in 3D problems, has become a bottleneck which blocks its further application in real engineering problems. Main factors affecting the computational efficiency of the rigid-plastic meshless method are analysed and the half band width formulation is proposed. The 3D meshless analysis of bulk forming utilizing the half band width is proposed and realized. By adjusting the number of nodes in the definition domain and properly arranging the numbering of nodes, the calculation efficiency in meshless method can be improved greatly. Through the analysis of 3D numerical examples, it is shown that for simple 3D problems (the number of nodes is less than 1000), the calculation efficiency of FEM is evidently higher than that of RKPM while for complicated 3D problems which have much more nodes, the calculation time of RKPM versus that of FEM is about (1.5~2.0):1.