Research On Coupling Modeling Of Non-Ordinary State Based Peridynamics And Finite Element Method

Automobiles have entered the life of the public as a means of transportation.After the expansion of automobiles,automobile safety issues continue to expand.Among them,the study of fracture problems is of great significance for improving automobile safety.The finite element method(FEM)has defects when dealing with fracture problem,while the Peridynamics(PD)method can deal with discontinuity problem well.However,the PD computation efficiency is far inferior to the FEM.The coupling of PD method and traditional FEM can give full play to the advantages of the two theories,and it can also simulate the crack growth spontaneously while improving the calculation efficiency.At present,domestic and foreign researches are only using the theories of bond-based PD and ordinary state-based PD to couple FEM.Aiming at this situation,this paper proposes a coupling method of non-ordinary state-based PD theory and FEM.The main research contents are as follows:First of all,this paper summarizes the development status of PD method and explains the research status of PD method and FEM;then introduces the basic theory of non-ordinary state-based PD method and FEM.After that,based on the basic theoretical formula of the PD method,the implicit solution format for the non-ordinary state-based PD method is deduced,and then the implementation procedures are derived in detail.Specially,the calculation procedure of the coupling method is explained methodically through a simple local model.Afterward this article implements the whole calculation process by C ++ programming,and calculates several numerical examples of uniaxial stretching,pure shear,and transversale shear,respectively.By comparing the displacement of the measuring points obtained by the coupling method and the FEM,the applicability and accuracy of the proposed coupling method for uniform and non-uniform deformation are verified.Finally,the basic theory of the explicit central difference method is summarized.The crack propagation process of a brittle plate with pre-crack cracks is numerically simulated.By comparing the coupling results with the experimental ones,it is verified that the proposed coupling model in this paper is also effective for simulating the dynamic propagation of cracks.