Smoothed peridynamics for the extremely large deformation and cracking problems: Unification of peridynamics and smoothed particle hydrodynamics

Abstract Peridynamics (PD) and smoothed particle hydrodynamics (SPH) are definitely attractive theories in amounts of numerical mechanical methods these years, and numerous researchers have studied the similarities of these two methods. In this paper, the smoothed peridynamics (SPD) is proposed to unify these two theories in the meshless view. The SPD employs an update‐Lagrangian (UL) method, which is useful for the extremely large deformation and cracking problem. The SPD governing equation, nonlocal interaction, micro‐bond modules for elastic material are derived. In addition, the choice of the nonlocal kernel and logarithmic stretch is investigated. Finally, numerical experiments are studied to confirm the ability of SPD. The numerical results show that SPD has an excellent performance and application prospect in computational solid mechanics. Since the SPD model formulations are derived for general 3D conditions, it can be straight forwardly extended for large‐scale practical applications across disciplines.