Force flux and the peridynamic stress tensor

By R. Lehoucq, Stewart A. Silling. 2008

199 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/ac0518e5f8104cf59caf708330580c10cb7cbc4e

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In Civil and Structural Engineering

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

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, methodology): “From the mathematical point of view this procedure is applicable when the searched solution has a stronger regularity than the one strictly needed to formulate the basic variational principle.”
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].”
Variable Horizon in a Peridynamic Medium (2015, background): “As shown in [6], the peridynamic internal force density can be expressed without approximation as L = ∇ · ν where ν is the peridynamic stress tensor defined by ν(x) = 1 2 ∫”
A Unified Interpretation of Stress in Molecular Systems (2010, background): “Lehoucq and Silling [25] have recently shown that Noll’s solution is a minimum solution in a variational sense.”
A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities (2012, background): “Remark: Note that we could, possibly, define the heat-flux through the surface at a point by including all bonds passing through that surface, as it is done in in the peridynamic formulation for elasticity for the force fluxes ([78], [84]).”
Convergence, adaptive refinement, and scaling in 1D peridynamics (2009, background): “It reformulates the basic equations of motion in such a form that the internal forces are evaluated through an integral formulation that does not require the evaluation of a stress tensor field or its spatial derivatives [34].”
Convergence of Peridynamics to Classical Elasticity Theory (2008, methodology): “Previous results [24] have shown that the peridynamic equation of motion (1) expressed in the form ρ(x)ü(x, t) = ∫”
Peridynamic Theory of Solid Mechanics (2010, background): “Lehoucq and Silling [48] provide an expression (see (120) below) for the peridynamic stress tensor in terms of the bond force density.”