Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces

By Stewart A. Silling. 2000

3,981 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b047cc22192bc29267d0ce82f22752d006f06c34

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In Biomedical Engineering

In Mechanics of Materials

Citations in the corpus

The effect of long-range forces on the dynamics of a bar (2005, methodology): “The general theory that describes our setting, including the accompanying equation of motion, was developed independently by Kunin [3], Rogula [4] and Silling [5], and is called the peridynamic theory.”
Viscoplasticity using peridynamics (2010, background): “It has been shown that if the analyst is only interested in the bulk response of the material, then the choice of is essentially arbitrary [1].”
On the Evolutionary Fractional p-Laplacian (2015, neutral): “, [12, 30]).”
A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows (2017, positive): “To demonstrate the exibility of SAV approach, we will focus on a free energy with a nonlocal 14 J. SHEN, J. XU, J. YANG kernel. Specically, we replace the Laplacian by a nonlocal linear operator L [67]: L ˚(x) = Z B(x;) ˆ (jy xj) ˚(y) ˚(x) dy; leading to the free energy, (3.8) E(˚) = Z ˆ 1 4 ˚4 + 1”
Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems (2013, background): “1 Introduction Nonlocal models are currently used in a large variety of applications, including continuum mechanics [18, 39], graph theory [33], nonlocal wave equations [40], and jump processes [9, 10, 15].”
At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola (2013, background): “In [120] the analysis started by Piola is continued, seemingly as if the author, Silling, were one of his closer pupils: arguments are very similar and also a variational formulation of the presented theories is found and discussed.”
Force flux and the peridynamic stress tensor (2008, background): “The peridynamic model [5] is an alternative theory of continuum mechanics based on integral, rather than differential, equations.”
A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities (2012, background): “In principle, since the peridynamic formulation is nonlocal, such boundary conditions are imposed over a layer of thickness δ, the peridynamic horizon, inside the surface of the body (see [26]).”
Crack nucleation in variational phase-field models of brittle fracture (2018, neutral): “Models based on the peridynamics theory [87] may present an alternative way to handle these issues, but to our knowlege, they are still falling short of providing robust quantitative predictions at the structural scale.”
Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory (2009, methodology): “It is worth remarking that long-range interaction forces depending on the relative displacements between non-adjacent elements may be found in the so-called peridynamic method in elasticity [ 32 , 33], previously formulated to account for the presence of cracks, dislocations and discontinuity in the”
Peridynamics via finite element analysis (2007, background): “012 has been proposed that does not require spatial derivatives to be evaluated within a body [1–6].”