Nonlocal matching boundary conditions for non-ordinary peridynamics with correspondence material model

A class of Nonlocal Matching Boundary Condition (NMBC) is presented for multiscale analysis that employs non-ordinary peridynamics (NOPD) with correspondence material model. The NMBC is cast in the form of parameterized expressions involving displacements and their higher-order time derivatives of the peridynamic (PD) nodes at the numerical interface. The corresponding parameters are solved by zeroing the associated residual and its higher order derivatives that are functions of the dispersion relation at the particular wave length of interest. After deriving the dispersion relations for both the standard and stabilized versions of NOPD with the correspondence material model, NMBCs are established for both 1D and 2D and the robustness is demonstrated in numerical examples. It is shown that stabilized NOPD effectively reduces the effects of the zero energy modes in the standard NOPD. Furthermore, nonlocal implementation is essential in eliminating the edge effects at the interface.