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.
The general particle dynamics (GPD), which is based on the kernel approximation method and Navier–Stokes equation, was developed from smoothed‐particle hydrodynamics to simulate the fracture behaviors by using the collective of damage variable to describe the damage evolution behaviors. In this paper, an advanced GPD with a nonlocal foundation is proposed for better description of the solid mechanics. The nonlocal vector calculus and microscopic constitutive model are employed to derive the governing equations in the proposed theory. The novel GPD with a nonlocal core is a generalization, which permits the inclusion of the microscopic constitutive model and the multi‐scale modeling compared with the previous GPD. To accomplish this generalization, the relationship between GPD and the previous kernel‐based theory is established. The novel GPD is superior in the fracture problems and multi‐scale modeling. Some numerical experiments are launched to verify the ability of the novel GPD.
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