Numerical Tools for Improved Convergence of Meshfree Peridynamic Discretizations

  • Pablo SelesonEmail author
  • David J. Littlewood
Living reference work entry


Peridynamic models have been employed to simulate a broad range of engineering applications concerning material failure and damage, with the majority of these simulations using a meshfree discretization. This chapter reviews that meshfree discretization, related issues present in peridynamic convergence studies, and possible remedies proposed in the literature. In particular, we discuss two numerical tools, partial-volume algorithms and influence functions, to improve the convergence behavior of numerical solutions in peridynamics. Numerical studies in this chapter involve static and dynamic simulations for linear elastic state-based peridynamic problems.


Peridynamics Meshfree discretization Partial volumes Influence functions Convergence Statics Dynamics 



This study was supported in part by the Householder Fellowship which is jointly funded by: the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program, under award number ERKJE45, and the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory (ORNL), which is operated by UT-Battelle, LLC., for the U.S. Department of Energy under Contract DE-AC05-00OR22725; and by the Laboratory Directed Research and Development program at Sandia National Laboratories, which is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.


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Copyright information

© Springer International Publishing AG (outside the USA) 2018

Authors and Affiliations

  1. 1.Computer Science and Mathematics DivisionOak Ridge National LaboratoryOak RidgeUSA
  2. 2.Center for Computing ResearchSandia National LaboratoriesAlbuquerqueUSA

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