Peridynamic operator method

Abstract

We propose a so-called Peridynamic operator method (PDOM) which can convert the local differentiation or its products into the nonlocal integral form. We will show that the peridynamic differential operator (PDDO) or nonlocal operator method (NOM) is a special case of this proposed PDOM. PDOM is derived for elasticity problems in two different ways: a) based on variational principles and b) Lagrange’s equations. For spherical integral domains, PDOM recovers all types of Peridynamics (PD) and Dual-horizon Peridynamics (DH-PD) formulations. We also present a simple and efficient approach without zero-energy modes and develop PDOM for scattered data, ordinary and partial differential equations. One key feature of this approach is that it does not require any special treatment in the presence of discontinuities or singularities. Several numerical examples are presented to verify the capability of the proposed method.