Coupling of Peridynamics and Numerical Substructure Method for Modeling Structures with Local Discontinuities

Peridynamics(PD)is a widely used theory to simulate discontinuities,but its application in real-world structural problems is somewhat limited due to the relatively low-efficiency.The numerical substructure method(NSM)presented by the authors and co-workers provides an efficient approach for modeling structures with local nonlinearities,which is usually restricted in problems of continuum mechanics.In this paper,an approach is presented to couple the PD theory with the NSM for modeling structures with local discontinuities,taking advantage of the powerful capability of the PD for discontinuities simulation and high computational efficiency of the NSM.The structure is simulated using liner elastic finite element(FE)model while the local cracking regions are isolated and simulated using a PD substructure model.A force corrector calculated from the PD model is applied on the FE model to consider the effect of discontinuities.The PD is integrated in the substructure model using interface elements with embedded PD nodes.The equations of motions of both the NSM system and the PD substructure are solved using the central difference method.Three examples of two-dimensional(2D)concrete cantilever beams under the concentrated force are investigated to verify the proposed coupling approach.