An effective correspondence-based peridynamics-FEM coupling model for brittle fracture

Abstract

Correspondence-based peridynamics (CBPD) is attractive and promising because of its outstanding ability to employ the traditional constitutive relations for material modeling. However, application of CBPD to brittle fracture problems is somewhat limited due to the numerical instability issue and lack of a rational bond failure criterion. To enable CBPD to accurately and stably predict brittle fracture problems, an improved energy-based bond failure criterion is firstly established in this work, in which the expression of bond potential is re-derived, and its simplified expression for isotropic linear elastic solids is clearly defined. The critical bond potential is determined by assuming it is directly proportional to the bond length, and the discretization error for the critical energy release rate in the discretized model is corrected with a correction factor. Besides the zero-energy mode control method, additional stabilization technique to reduce the influence of ill-posed or singular reference shape tensor on brittle fracture simulations is also explored to avoid the unexpected irregular damages during the fracture process. In addition, a direct coupling model of CBPD and FEM is established to improve the computational efficiency, and the ghost forces at the interface are verified to be negligible. Finally, several numerical examples involving typical quasi-static and dynamic brittle fracture problems are investigated, and fracture behaviors including the crack paths, load-displacement curves, and crack propagation speeds are all well predicted, which sufficiently demonstrates the accuracy and stability of the proposed method.