Imposition of local boundary conditions in peridynamics without a fictitious layer and unphysical stress concentrations

Deepak Behera, Pranesh Roy, Sundaram Vinod K. Anicode, Erdogan Madenci, Benjamin Spencer

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


This study introduces a general approach for the imposition of local boundary conditions in non-ordinary state-based peridynamics (NOSB PD) to eliminate the displacement kinks near the boundary without a fictitious layer under quasi-static loading conditions. It identifies the underlying reason for the unphysical displacement kinks. Under an imposed linear displacement field, the NOSB PD equilibrium equation is not satisfied near the boundary due to the unsymmetric horizon of material points. However, the equilibrium equation derived by using the PD differential operator is satisfied at such material points. Therefore, the material body is divided into three regions to satisfy the equilibrium equations and to impose displacement and tractions boundary conditions. This approach does not deviate from the original NOSB PD; however, it provides a simple solution to eliminate the displacement kink near the boundary, which leads to unphysical stress concentrations. Its efficacy is demonstrated by considering elastic rectangular and square plates subjected to various types of boundary conditions leading to homogeneous as well as nonhomogeneous deformations. The creep response of a rectangular plate further proves the robustness of the present approach. Also, a quasi-static crack propagation from a pre-existing crack in a square plate under mode-I, mode-II and mixed-mode loading conditions demonstrates its capability for failure prediction based on the critical stretch criteria. Finally, its applicability for 3D analysis is demonstrated by considering a rectangular prism under applied stretch and normal stress.

Original languageEnglish (US)
Article number114734
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Apr 1 2022


  • Boundary conditions
  • Displacement
  • Nonlocal
  • Peridynamics
  • Traction

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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