International Journal of Fracture

, Volume 176, Issue 2, pp 195–206

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

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

DOI: 10.1007/s10704-012-9745-8

Cite this article as:
Hu, W., Ha, Y.D., Bobaru, F. et al. Int J Fract (2012) 176: 195. doi:10.1007/s10704-012-9745-8

Abstract

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.

Keywords

J-integralPeridynamicsNonlocal methodsPath-independenceFracture

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Wenke Hu
    • 1
  • Youn Doh Ha
    • 1
    • 3
  • Florin Bobaru
    • 1
  • 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