Crack nucleation in a peridynamic solid

Abstract

A condition for the emergence of a discontinuity in an elastic peridynamic body is proposed, resulting in a material stability condition for crack nucleation. The condition is derived by determining whether a small discontinuity in displacement, superposed on a possibly large deformation, grows over time. Stability is shown to be determined by the sign of the eigenvalues of a tensor field that depends only on the linearized material properties. This condition for nucleation of a discontinuity in displacement can be interpreted in terms of the dynamic stability of plane waves with very short wavelength. A numerical example illustrates that cracks in a peridynamic body form spontaneously as the body is loaded.

An approach for incorporating classical continuum damage models in state-based peridynamics

“…A particle-based discretization of peridynamic was proposed in [4], where it was demonstrated that the critical bond elongation u c can be related to the fracture energy G 0 for brittle materials. This approach has been used for modeling fracture and failure of composites, nanofiber networks and polycrystals [5], to simulate ballistic impact on brittle plates [6], to study crack nucleation in peridynamic solids [7], and to study dynamic crack propagation and crack branching [8]. The main limitation of the bond-based peridynamic theory is that it only considers pairwise interactions between particles.…”

“…Within the context of ordinary state-based peridynamics, the role of the influence function has been explored in [12], and a critical bond elongation criterion has been proposed in [11] which is similar to the damage modeling approach commonly used in bond-based peridynamics [3,4,5,6,7,8].…”

Mathematical analysis for the peridynamic nonlocal continuum theory

“…Indeed, PD can be effectively used in the multiscale modeling of materials in different ways: it can serve as a bridge between molecular dynamics (MD) and continuum elasticity (CE) to help mitigate the difficulties encountered when one attempts to couple MD and CE directly [4,5,11,15,18] and, in some situations, PD can be used as a stand-alone model to capture the behavior of materials over a wide range of spatial and temporal scales. For example, to study problems involving defects, one can use the same equations of motion over the entire body and no special treatment is needed near or at defects [6,22].…”

Peridynamic Modeling and Simulation of Rolling Contact Fatigue

“…It has been applied to structural stability and failure analyses [11,12], fracture mechanics [13][14][15][16], and composite materials [17][18][19][20]. In this paper, we employed peridynamics to study rolling contact fatigue.…”