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

Authors

• Wenke Hu, University of Nebraska-LincolnFollow
• Youn Doh Ha, Kunsan National University, Korea
• Florin Bobaru, University of Nebraska-LincolnFollow
• Stewart A. Silling, Sandia National Laboratories, NM

Document Type

Article

Date of this Version

2012

Citation

Int J Fract (2012) 176:195–206; DOI 10.1007/s10704-012-9745-8

Comments

US Govt work.

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.