On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity

By Etienne Emmrich, Olaf Weckner. 2007

188 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a1d80f7284235fe0a13f9511d231d21d11114735

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Convergence of Peridynamics to Classical Elasticity Theory (2008, background): “Emmrich and Weckner [23] also proved convergence of the bond-based peridynamic equation of motion to the classical Navier equation of motion for a homogeneous linear isotropic microelastic solid.”
Analysis of the Volume-Constrained Peridynamic Navier Equation of Linear Elasticity (2013, background): “Results similar to those in Theorem 4 have been established for the peridynamic bond-based model; see for instance, [4,11,12].”
A physics-informed variational DeepONet for predicting the crack path in brittle materials (2021, background): “Newer alternatives such as phase-ﬁeld [1–4] and peridynamics [5–10] models have been able to predict the outcome of carefully controlled experiments; however, the complexity of those models comes at a substantially higher computational cost.”
Surface corrections for peridynamic models in elasticity and fracture (2017, background): “been shown that the peridynamic model of solid mechanics converges to classical elasticity theory when the horizon goes to zero [4,5].”
Continuous and discontinuous finite element methods for a peridynamics model of mechanics (2011, background): “For the special case of proportional materials [11, 13, 26], it follows from (2.”
Peridynamic Theory of Solid Mechanics (2010, methodology): “Weckner and Emmrich investigated certain discretizations of the peridynamic equation of motion, including Gauss-Hermite quadrature, and applied these to initial value problems to demonstrate convergence [78] [22].”
Linearized Theory of Peridynamic States (2010, background): “7 Limit of Small Horizon It was shown in [7] and more generally in [10] that if a deformation of a body is classically smooth, then the peridynamic theory converges to the standard theory in the limit δ → 0.”