Computational Mechanics

, Volume 53, Issue 6, pp 1251–1264 | Cite as

A meshfree unification: reproducing kernel peridynamics

  • M. A. Bessa
  • J. T. Foster
  • T. Belytschko
  • Wing Kam LiuEmail author
Original Paper


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.


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



This work was funded in part by grants from the United States Air Force Office of Scientific Research grant number W911NF-11-1-0208 and National Energy Technology Laboratory grant number DE-FE0010808.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • M. A. Bessa
    • 1
  • J. T. Foster
    • 2
  • T. Belytschko
    • 1
  • Wing Kam Liu
    • 1
    Email author
  1. 1.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA
  2. 2.Mechanical Engineering DepartmentThe University of Texas at San AntonioSan AntonioUSA

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