Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach

Bobaru, Florin

doi:10.1088/0965-0393/15/5/002

Cited by 92 publications

(67 citation statements)

References 41 publications

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“…The method is particularly well suited for dealing with cracks and damage in solid mechanics (see [25,26]) especially in situations where the crack path, for example, is not known in advance. The method also allows for easy introduction of longrange forces, such as van der Waals interactions and examples of deformation and damage at the nanoscale are treated in [26,27]. In fact, all forces in the peridynamic formulation are long-range.…”

Section: Overview Of Peridynamicsmentioning

confidence: 99%

Convergence, adaptive refinement, and scaling in 1D peridynamics

Bobaru

Yang

Alves

et al. 2008

Numerical Meth Engineering

448

331

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SUMMARYWe introduce here adaptive refinement algorithms for the non-local method peridynamics, which was proposed in (J. Mech. Phys. Solids 2000; 48:175-209) as a reformulation of classical elasticity for discontinuities and long-range forces. We use scaling of the micromodulus and horizon and discuss the particular features of adaptivity in peridynamics for which multiscale modeling and grid refinement are closely connected. We discuss three types of numerical convergence for peridynamics and obtain uniform convergence to the classical solutions of static and dynamic elasticity problems in 1D in the limit of the horizon going to zero. Continuous micromoduli lead to optimal rates of convergence independent of the grid used, while discontinuous micromoduli produce optimal rates of convergence only for uniform grids. Examples for static and dynamic elasticity problems in 1D are shown. The relative error for the static and dynamic solutions obtained using adaptive refinement are significantly lower than those obtained using uniform refinement, for the same number of nodes.

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Section: Overview Of Peridynamicsmentioning

confidence: 99%

Convergence, adaptive refinement, and scaling in 1D peridynamics

Bobaru

Yang

Alves

et al. 2008

Numerical Meth Engineering

448

331

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“…Regardless of the exact value of δ, the peridynamic equations retain their applicability on crack tips and surfaces. If it is additionally required to reproduce effects controlled by small-scale behavior, such as dispersion curves, then δ must be chosen to reflect the relevant physical length scale [5][6][7]. An example of a physically determined length scale is the spacing of aggregate in concrete; Bazant has shown that a suitable nonlocal model for concrete has advantages over a homogenized local model in the prediction of damage and localization [8].…”

Section: Length Scales Nonlocality and Continuamentioning

confidence: 99%

Convergence of Peridynamics to Classical Elasticity Theory

2008

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The peridynamic model of solid mechanics is a nonlocal theory containing a length scale. It is based on direct interactions between points in a continuum separated from each other by a finite distance. The maximum interaction distance provides a length scale for the material model. This paper addresses the question of whether the peridynamic model for an elastic material reproduces the classical local model as this length scale goes to zero. We show that if the motion, constitutive model, and any nonhomogeneities are sufficiently smooth, then the peridynamic stress tensor converges in this limit to a PiolaKirchhoff stress tensor that is a function only of the local deformation gradient tensor, as in the classical theory. This limiting Piola-Kirchhoff stress tensor field is differentiable, and its divergence represents the force density due to internal forces. The limiting, or collapsed, stress-strain model satisfies the conditions in the classical theory for angular momentum balance, isotropy, objectivity, and hyperelasticity, provided the original peridynamic constitutive model satisfies the appropriate conditions.

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“…Propagation, as opposed to nucleation, of cracks within the peridynamic model has been described elsewhere (Silling and Askari 2005) and has been applied to a number of problems involving complex patterns of fracture (Silling 2003;Silling and Bobaru 2005;Askari et al 2006;Bobaru 2007;Xu et al 2007;Colavito et al 2007;Gerstle et al 2007;Xu et al 2008;Agwai et al 2008a,b;Agwai et al 2009). Crack growth occurs through the irreversible breakage of bonds as they stretch in the vicinity of a crack tip.…”

Section: Introductionmentioning

confidence: 99%

Crack nucleation in a peridynamic solid

Silling¹,

Weckner²,

Askari³

et al. 2010

IUTAM Symposium on Dynamic Fracture and Fragmentation

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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.

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Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach

Cited by 92 publications

References 41 publications

Convergence, adaptive refinement, and scaling in 1D peridynamics

Convergence, adaptive refinement, and scaling in 1D peridynamics

Convergence of Peridynamics to Classical Elasticity Theory

Crack nucleation in a peridynamic solid

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