, Volume 53, Issue 14, pp 3495–3515 | Cite as

Bond-based peridynamic modelling of singular and nonsingular crack-tip fields

  • Roberto Ballarini
  • Vito DianaEmail author
  • Luigi Biolzi
  • Siro Casolo


A static meshfree implementation of the bond-based peridynamics formulation for linearly elastic solids is applied to the study of the transition from local to nonlocal behavior of the stress and displacement fields in the vicinity of a crack front and other sources of stress concentration. The long-range nature of the interactions between material points that is intrinsic to and can be modulated within peridynamics enables the smooth transition from the square-root singular stress fields predicted by the classical (local) linear theory of elasticity, to the nonsingular fields associated with nonlocal theories. The accuracy of the peridynamics scheme and the transition from local to nonlocal behavior, which are dictated by the lattice spacing and micromodulus function, are assessed by performing an analysis of the boundary layer that surrounds the front of a two dimensional crack subjected to mode-I loading and of a cracked plate subjected to far-field tension.


Discrete approach Non-local elasticity Peridynamics Stress Mode I crack fields 


Compliance with ethical standards

Conflict of interest

Roberto Ballarini is Associate Editor of Meccanica. The authors declare that they have no other conflicts of interest.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of HoustonHoustonUSA
  2. 2.Department ABCPolitecnico di MilanoMilanItaly

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