Convergence of Peridynamics to Classical Elasticity Theory

By Stewart A. Silling, R. Lehoucq. 2008

495 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/864780cb5b2bcad2b00a4430148368a300dd0766

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Citations in the corpus

The Meaning, Selection, and Use of the Peridynamic Horizon and its Relation to Crack Branching in Brittle Materials (2012, methodology): “The microelastic peridynamic model or the peridynamic model of heat transfer converge, in the limit of the horizon going to zero, to the corresponding classical models (see Silling and Lehoucq 2008, Bobaru et al. 2009, Bobaru and Duangpanya 2010).”
A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities (2012, unknown): “, [83]).”
Dual‐horizon peridynamics (2015, background): “ond-based formulation (BB-PD) where the bonds behave like springs and independent of each other. BB-PD can be regarded as a special case of a more general theory, the state-based peridynamics (SB-PD) [2, 14] which can be suited for, theoretically, any type of constitutive model and large deformation”
Implementing peridynamics within a molecular dynamics code (2007, methodology): “Future work involves computing thermodynamic quantities such as temperature, computing the PD stress given by [6], implementing the more general PD state theory [17] to go beyond central force interactions, and the simulation of classical elasticity given by the results of [19].”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “Peridy-namics has been shown to converge to the local model when the length-scale goes to zero (Silling and Lehoucq 2008).”
Peridynamic Theory of Solid Mechanics (2010, background): “It is easily shown [68] that this force state scales with s as follows: T̂s(Ys)〈ξ〉 = sT̂1 ( Es(Ys) ) 〈ξ/s〉 ∀ξ ∈ Hs.”
Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites (2012, background): “In δ-convergence we expect the nonlocal solutions to converge to the classical, local solutions (see [34, 37]).”
The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions (2010, methodology): “A step in this direction has been recently made by Silling and co-workers (Silling, 2000; Silling et al., 2003; Silling and Lehoucq, 2008).”
A force-based coupling scheme for peridynamics and classical elasticity (2013, background): “In [40], it is shown that under appropriate differentiability assumptions, (1) can be expressed in the form (5) by replacing σ with a nonlocal stress tensor.”
Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening (2016, background): “ Hence, the classical theory of elasticity can be considered a limiting case of the peridynamic theory as the horizon approaches zero (Silling and Lehoucq, 2008).”
Variable Horizon in a Peridynamic Medium (2015, background): “As discussed in [19], the collapsed stress tensor is a legitimate Piola stress tensor whose constitutive model depends on the local deformation gradient tensor through (8).”