A two‐dimensional ordinary, state‐based peridynamic model for linearly elastic solids. (3rd March 2014)

• Record Type: Journal Article
• Authors: Le, Q.V.; Chan, W.K.; Schwartz, J.
• Is Part Of: International journal for numerical methods in engineering. Volume 98:Number 8(2014)
• Page Start: 547
• Page End: 561
• Publication Date: 2014-03-03
• Subjects: Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.4642
• Languages: English
• ISSNs: 0029-5981

Abstract

<abstract abstract-type="main" id="nme4642-abs-0001"> <title>SUMMARY</title> <p id="nme4642-para-0001">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 <italic>m</italic>‐convergence and <italic>δ</italic>‐convergence behaviors when <italic>m</italic> increases and <italic>δ</italic> 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 &amp; Sons, Ltd.</p> </abstract>