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A two‐dimensional ordinary , state‐based peridynamic model for linearly elastic solids
Author(s) -
Le Q.V.,
Chan W.K.,
Schwartz J.
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4642
Subject(s) - peridynamics , classification of discontinuities , dynamic relaxation , plane (geometry) , constant (computer programming) , finite element method , convergence (economics) , mechanics , plane stress , stress (linguistics) , constitutive equation , mathematical analysis , compression (physics) , mathematics , materials science , physics , geometry , continuum mechanics , computer science , thermodynamics , linguistics , philosophy , economics , programming language , economic growth
SUMMARY Peridynamics is a non‐local mechanics theory that uses integral equations to include discontinuities directly in the constitutive equations. A three‐dimensional, state‐based peridynamics model has been developed previously for linearly elastic solids with a customizable Poisson's ratio. For plane stress and plane strain conditions, however, a two‐dimensional model is more efficient computationally. Here, such a two‐dimensional state‐based peridynamics model is presented. For verification, a 2D rectangular plate with a round hole in the middle is simulated under constant tensile stress. Dynamic relaxation and energy minimization methods are used to find the steady‐state solution. The model shows m ‐convergence and δ ‐convergence behaviors when m increases and δ decreases. Simulation results show a close quantitative matching of the displacement and stress obtained from the 2D peridynamics and a finite element model used for comparison. Copyright © 2014 John Wiley & Sons, Ltd.