The formulation and computation of the nonlocal J-integral in bond-based peridynamics
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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.
KeywordsJ-integral Peridynamics Nonlocal methods Path-independence Fracture
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- Bobaru F, Hu W (2012) The meaning, selection, and use of the peridynamic horizon and its relation to crack branching in brittle materials. Int J Fract. doi: 10.1007/s10704-012-9725-z
- Foster JT, Silling SA, Chen WW (2010) Viscoplasticity using peridynamics. Int J Numer Meth Eng 81: 1242–1258Google Scholar
- Hu W, Ha YD, Bobaru F (2012) Peridynamic simulations of dynamic fracture in unidirectional fiber-reinforced composites. Comput Methods Appl Mech Eng. 217–220: 247–261Google Scholar
- Kilic B (2008) Peridynamic theory for progressive failure prediction in homogeneous and heterogeneous materials. Ph.D. thesis, Department of Aerospace and Mechanical Engineering, University of Arizona, pp 68Google Scholar