Convergence, adaptive refinement, and scaling in 1D peridynamics

By Florin Bobaru, Mijia Yang, Leonardo Fuchs Alves, Stewart A. Silling, E. Askari, Jifeng Xu. 2009

551 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/d41497d6bb9a331233de3ac51c546c26dd3d21d1

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Surface corrections for peridynamic models in elasticity and fracture (2017, methodology): “In other studies ([4,20,39,40]), it has been shown that the discrete PD model converges to the continuum PD”
Numerical solution of linear and nonlinear partial differential equations using the peridynamic differential operator (2017, methodology): “The convergence of the solutions is based on the δ− convergence analysis [7].”
Impact Mechanics and High-Energy Absorbing Materials: Review (2008, background): “Silling et al. (2003) and Bobaru et al. (2008) discuss the peridynamic formulation for a one-dimensional bar, and the convergence of the peridynamic solution to the classical one in the limit of short-range forces is shown.”
Dual‐horizon peridynamics (2015, background): “studied the convergence and adaptive refinement in 1D peridynamics [33] and multi-scale modeling in 2D BB-PD [34].”
Why do cracks branch? A peridynamic investigation of dynamic brittle fracture (2015, background): “For examples of micromodulus functions in 3D see Silling and Askari (2005), in 2D see Ha and Bobaru (2010), and in 1D see Bobaru et al. (2009).”
Peridynamic Theory of Solid Mechanics (2010, methodology): “Adaptive refinement and convergence of the discretized method in one dimension are discussed in [11].”
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).”
Continuous and discontinuous finite element methods for a peridynamics model of mechanics (2011, background): “†In [6], effective adaptive grid refinement strategies are discussed for a discretization of (2.”