Smoothed Bond-Based Peridynamics

Advanced general particle dynamics with nonlocal foundation for fracture analysis

“…[10][11][12][13][14] In the same time, the theoretical analysis of GPD on the traditional continuum level is under a rapid development, Yao et al 15 pointed out the deficiency of the kernel in GPD and modified the kernel approximation in his novel continuous smoothed-particle hydrodynamics (CSPH) theory. Zhou et al 16,17 extended the GPD theory in the micro-level with the combination of the peridynamics (PD) and proposed a novel smoothed PD (SPD). Bessa et al 18 proposed a meshfree unification reproducing kernel PD and investigated the relationship between the kernel approximation, meshless PD method, and other meshfree methods.…”

“…The traditional GPD belongs to the classical continuum mechanics, which does not fully consider the scale and material microstructure influences on macroscopic mechanical properties, so it cannot effectively explain some phenomenon and problems that the classical theory is difficult to explain, such as deformation localization, the crack tip stress singularity, and high frequency wave scattering. 16 To get rid of this predicament, various numerical algorithms are developed to amend these problems. 15,21 This is also the reason why a lot of the novel continuum mechanic-based numerical theories need to develop for handling these problems, such as phase-field method, 22,23 the extend finite element method, 24,25 smoothed finite element method, 26 and micromechanical finite element method.…”

“…The PD description, which uses integral differential equations (IDEs), converges to the traditional PDE theory where there are no discontinuities; in this sense, PD provides a generalization of the PDE theory that enables to directly simulate the fracture process and has capability of modeling crack initiation, propagation, bifurcation, coalescence, and separation. 16,17 In this view of point, nonlocal theory is a generalization of the traditional continuum theory and can resolve many problems that for the traditional theory is hard to handle. In recent years, nonlocal theory is in frontier research and undergoes a rapid development among the various research interests, for example, physical mechanics, 31,32 sociologies, 33,34 artificial intelligence 35,36 and medical images.…”

“…In the present solid physics, the research target is to study the macroscopic properties and laws of solids from the micro level. The traditional GPD belongs to the classical continuum mechanics, which does not fully consider the scale and material microstructure influences on macroscopic mechanical properties, so it cannot effectively explain some phenomenon and problems that the classical theory is difficult to explain, such as deformation localization, the crack tip stress singularity, and high frequency wave scattering 16 . To get rid of this predicament, various numerical algorithms are developed to amend these problems 15,21 .…”

“…In solid mechanics, the theory of PD 31 was proposed as a possible alternative to the conventional models of elasticity and fracture mechanics. The PD description, which uses integral differential equations (IDEs), converges to the traditional PDE theory where there are no discontinuities; in this sense, PD provides a generalization of the PDE theory that enables to directly simulate the fracture process and has capability of modeling crack initiation, propagation, bifurcation, coalescence, and separation 16,17 . In this view of point, nonlocal theory is a generalization of the traditional continuum theory and can resolve many problems that for the traditional theory is hard to handle.…”