Coupling of peridynamics with finite elements for brittle fracture problems in irregular meshgrids

Abstract

A PD-FEM coupling scheme with the potential to solve large-scale or multi-scale models is proposed which utilizes the advantages of PD in solving discontinuities and the computational efficiency of the finite element method. The scheme can perform the global unstructured discretization of the model, ensure that the crack initiation and propagation are not affected by the grid, and the boundary conditions can be flexibly arranged. The non-overlapping domain coupling method is used to couple the finite element domain and the circumferential dynamic domain to reduce the influence of the ghost force on the model solution. In order to verify the ghost force, the proposed PD-FEM model is used to simulate the displacement field distribution of the two-dimensional plate under uniaxial tension and the cantilever beam under concentrated force. The calculation results are compared with the theoretical calculation results and finite element calculation results. In addition, the scheme takes advantage of the high computational efficiency of the finite element method, and uses the OpenMP parallel computing framework of Fortran language to realize the efficient solution of the three-dimensional model. The validity and computational efficiency of the PD-FEM model are verified by the tensile test of the prefabricated cracked square plate, the double-notched specimen, the three-dimensional l-shaped plate and the composite mode fracture test of the three-dimensional three (four) point bending beam.