A meshfree unification: Reproducing kernel peridynamics

M. A. Bessa, J. T. Foster, T. Belytschko, Wing Kam Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

138 Scopus citations


This paper is the first investigation establishing the link between the meshfree state-based peridynamics method and other meshfree methods, in particular with the moving least squares reproducing kernel particle method (RKPM). It is concluded that the discretization of state-based peridynamics leads directly to an approximation of the derivatives that can be obtained from RKPM. However, state-based peridynamics obtains the same result at a significantly lower computational cost which motivates its use in large-scale computations. In light of the findings of this study, an update to the method is proposed such that the limitations regarding application of boundary conditions and the use of non-uniform grids are corrected by using the reproducing kernel approximation.

Original languageEnglish (US)
Pages (from-to)1251-1264
Number of pages14
JournalComputational Mechanics
Issue number6
StatePublished - Jun 2014


  • Meshfree methods
  • Moving least squares
  • Reproducing kernel
  • State-based peridynamics
  • Strong form discretization
  • Weak form discretization

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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