Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Two-dimensional implementation of the coarsening method for linear peridynamics

Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, 100 Montrose Street, Glasgow G4 0LZ, UK

Special Issues: Peridynamics

Peridynamic theory was introduced to overcome the limitations of classical continuum mechanics (CCM) in handling discontinuous material response. However, for certain problems, it is computationally expensive with respect to CCM based approaches. To reduce the computational time, a coarsening method was developed and its capabilities were demonstrated for one-dimensional structures by substituting a detailed model with a surrogate model with fewer degrees of freedom. The objective of this study is to extend the application of coarsening method for linear peridynamics for two-dimensional analysis. Moreover, the existing one-dimensional coarsening method was further explored by considering various different micromodulus functions. The numerical results demonstrated that coarsening approach has a potential to reduce the computational time with high accuracy for both one-dimensional and two-dimensional problems.
  Article Metrics

Keywords peridynamics; coarsening; non-local; numerical; composite

Citation: Yakubu Galadima, Erkan Oterkus, Selda Oterkus. Two-dimensional implementation of the coarsening method for linear peridynamics. AIMS Materials Science, 2019, 6(2): 252-275. doi: 10.3934/matersci.2019.2.252


  • 1. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48: 175–209.    
  • 2. Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83: 1526–1535.    
  • 3. Silling SA, Zimmermann M, Abeyaratne R (2003) Deformation of a Peridynamic Bar. J Elasticity 73: 173–190.    
  • 4. Ha YD, Bobaru F (2011) Characteristics of dynamic brittle fracture captured with peridynamics. Eng Fract Mech 78: 1156–1168.    
  • 5. Parks ML, Lehoucq RB, Plimpton SJ, et al. (2008) Implementing peridynamics within a molecular dynamics code. Comput Phys Commun 179: 777–783.    
  • 6. Chen X, Gunzburger M (2011) Continuous and discontinuous finite element methods for a peridynamics model of mechanics. Comput Method Appl M 200: 1237–1250.    
  • 7. Ghajari M, Iannucci L, Curtis P (2014) A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media. Comput Method Appl M 276: 431–452.
  • 8. Huang D, Lu GD, Wang CW, et al. (2015) An extended peridynamic approach for deformation and fracture analysis. Eng Fract Mech 141: 196–211.    
  • 9. Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fracture 162: 229–244.    
  • 10. Agwai A, Guven I, Madenci E (2011) Predicting crack propagation with peridynamics: a comparative study. Int J Fracture 171: 65.    
  • 11. Bobaru F, Ha YD (2011) Adaptive refinement and multiscale modeling in 2D peridynamics. J Multiscale Com 9: 635–659.    
  • 12. Rahman R, Foster JT, Haque A (2014) A multiscale modeling scheme based on peridynamic theory. Int J Multiscale Com 12: 223–248.    
  • 13. Silling SA (2011) A coarsening method for linear peridynamics. Int J Multiscale Com 9: 609–622.    
  • 14. Bobaru F, Yang M, Alves LF, et al. (2009) Convergence, adaptive refinement, and scaling in 1D peridynamics. Int J Numer Meth Eng 77: 852–877.    


This article has been cited by

  • 1. N. Zhu, E. Oterkus, Calculation of Stress Intensity Factor using Displacement Extrapolation Method in Peridynamic Framework, Journal of Mechanics, 2020, 1, 10.1017/jmech.2019.62

Reader Comments

your name: *   your email: *  

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved