International Journal of Fracture

, Volume 176, Issue 2, pp 195–206 | Cite as

The formulation and computation of the nonlocal J-integral in bond-based peridynamics

  • Wenke Hu
  • Youn Doh Ha
  • Florin BobaruEmail author
  • Stewart A. Silling
Original Paper


This work presents a rigorous derivation for the formulation of the J-integral in bond-based peridynamics using the crack infinitesimal virtual extension approach. We give a detailed description of an algorithm for computing this nonlocal version of the J-integral. We present convergence studies (m-convergence and δ-convergence) for two different geometries: a single edge-notch configuration and a double edge-notch sample. We compare the results with results based on the classical J-integral and obtained from FEM calculations that employ special elements near the crack tip. We identify the size of the nonlocal region for which the peridynamic J-integral value is near the classical FEM solutions. We discuss how the boundary conditions and the peridynamic “skin effect” may influence the peridynamic J-integral value. We also observe, computationally, the path-independence of the peridynamic J-integral.


J-integral Peridynamics Nonlocal methods Path-independence Fracture 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Wenke Hu
    • 1
  • Youn Doh Ha
    • 1
    • 3
  • Florin Bobaru
    • 1
    Email author
  • Stewart A. Silling
    • 2
  1. 1.Department of Mechanical & Materials EngineeringUniversity of Nebraska-LincolnLincolnUSA
  2. 2.Sandia National Laboratories, Multiphysics Simulation Technology DepartmentAlbuquerqueUSA
  3. 3.Department of Naval ArchitectureKunsan National UniversityKunsanKorea

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