Simulation Of 3D Metal Bulk Forming Based On Material Point Method

Metal bulk forming is an important means for machining metal parts.The forming process is a large deformation process,which involves geometric nonlinear and material nonlinear problems,so it must be solved by numerical method.As a new kind of meshless method,The Material Point Method(MPM)can not only overcome the mesh distortion of the Finite Element Method(FEM),but also avoid the disadvantages of the traditional meshless method,such as the large amount of computation,the difficulty of applying the essential boundary conditions,and the time consuming of the search particle.In this paper,the MPM is applied to the numerical simulation of the three-dimensional metal bulk forming,the upsetting and backward extrusion process were studied,and compared the results with the FEM and the traditional Element Free Galerkin Method(EFGM).The feasibility and effectiveness of the MPM in the numerical simulation of metal bulk forming processes are discussed.The specific contents of this paper are as follows:The weak form of the governing equation of the MPM and its discrete form are derived by using the weighted residual method.The explicit calculation process of the MPM is given.Based on the theory of metal elastic plastic and MPM,a method for solving the elastic plastic problem is established.The computation code is written and the accuracy of the algorithm and program is verified;The MPM is compared with the FEM and EFGM in terms of computational efficiency,accuracy and the results of different discrete points.It shows that the accuracy and efficiency of the MPM is similar to that of the FEM,but higher than that of the EFGM,what's more,the stability is higher than that of the EFGM when the particle number changed.Take the case of upsetting and backward extrusion process,the 3D bulk metal forming are studied by MPM.In the free upsetting simulation,the case of no friction contact and friction contact are analyzed,and compared the results with experiments and the FEM,it shows that they were in good agreement and verified the feasibility of the MPM for calculating the 3D bulk metal forming problems.In the simulation of backward extrusion,the deformed patterns and the variation of equivalent stress and equivalent strain are studied,and compared the results with the FEM and EFGM.The results shows that when punch stroke is small,both the MPM and FEM can well simulate the forming process,but when the stroke becomes larger the finite element mesh has a serious distortion in the simulation,which leads to the termination of the computation.However,the calculation of MPM is not affected,and the results are consistent with the EFGM.It can be seen that the MPM has great advantages than the FEM in the simulation of large deformation of metal bulk forming.The research provides some guidance for the numerical simulation of the MPM in other metal bulk forming processes.