A meshfree method based on the peridynamic model of solid mechanics

By Stewart A. Silling, E. Askari. 2005

2,431 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a9f3196f5c3fdc7cdb4417268173508ade88b219

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Crack nucleation in a peridynamic solid (2010, methodology): “As shown in Silling and Askari (2005), if bond breakage occurs at a prescribed value of bond stretch, then cracks advance according to the Griffith criterion, consuming a definite amount of energy per unit area.”
Continuous and discontinuous finite element methods for a peridynamics model of mechanics (2011, neutral): “, [4–6,15,16,27–30].”
Peridynamic Theory of Solid Mechanics (2010, methodology): “Additional examples, as well as more details about the numerical method, are discussed in [65] [76].”
Implementation of peridynamic beam and plate formulations in finite element framework (2018, neutral): “mainly utilizing meshless discretization concept [34].”
Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening (2016, background): “(50) Local damage, which defines the ratio of eliminated interactions to the total number of interactions associated with a material point within its horizon, can be calculated as (Silling and Askari, 2005) , , 1 H H t dV t dV x x x x .”
Dual-horizon peridynamics: A stable solution to varying horizons (2017, methodology): “In order to specify whether a bond is broken or not, a history-dependent scalar valued function μ is introduced [29], μ(t, ξ) =  1 if s(t , ξ) < s0 for all 0 ≤ t ′ ≤ t, 0 otherwise.”
An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis (2015, methodology): “According to the requirements concluded in [5,7,9,34], the kernel function gðξ; δÞ which reflects the distribution of the intensity of long-range forces in materials should hold the following relations:”
A morphing approach to couple state-based peridynamics with classical continuum mechanics (2016, background): “Peridynamics has been successfully applied to crack propagation [8, 12], investigating impact on a brittle solid [22], failure analyses of composites [2, 11] and nanotube reinforced composites [9].”
Convergence, adaptive refinement, and scaling in 1D peridynamics (2009, methodology): “A description of a meshfree numerical implementation for the peridynamic formulation is given in [25], where bond failure is related to the classical energy release rate in brittle fracture.”
Impact Mechanics and High-Energy Absorbing Materials: Review (2008, methodology): “Fragmentation due to impact on a thin brittle target is also modeled successfully in Silling and Askari (2005), Wei (2005), and Parks et al. (2008).”
Peridynamics for bending of beams and plates with transverse shear deformation (2015, background): “…determine the value of the bending critical curvature as 2 ( ) ( ) ( ) ( ) 1 1 1 2 K J b c j k k j k j Ic c V V G A x x (39) Based on the expression derived by Silling and Askari (2005) and Madenci and Oterkus (2013) for the critical energy release rate, it is evident that 4( )…”
Peridynamics simulations of geomaterial fragmentation by impulse loads (2015, background): “In the case of linear isotropic elastic materials, the critical bond stretch s0 can be related to the energy release rate in linear elastic fracture mechanics G0 [35], such that”