Peridynamic bond-associated correspondence model: Stability and convergence properties

Hailong Chen, Benjamin W. Spencer

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


The correspondence approach is a powerful technique that permits the usage of standard constitutive models from local theory within a peridynamic formulation. However, the conventional correspondence formulation suffers from material instability, ie, zero-energy modes, which must be controlled for it to be applied in practice. The recently-introduced correspondence reformulation based on the use of a bond-associated deformation gradient can inherently remove the material instability. In this paper, we show how the bond-associated correspondence model satisfies the requirement for material stability. The convergence behavior is also examined. The accuracy of this approach is further demonstrated by comparing model predictions against local reference solutions and results from the conventional correspondence model with penalty stabilization for both two-dimensional and three-dimensional problems.

Original languageEnglish
Pages (from-to)713-727
Number of pages15
JournalInternational Journal for Numerical Methods in Engineering
Issue number6
StatePublished - Feb 10 2019

Bibliographical note

Funding Information:
This work has been supported through the INL Laboratory Directed Research & Development (LDRD) Program under DOE Idaho Operation Office contract DE-AC07-05ID14517. This manuscript has been authored by Battelle Energy Alliance, LLC under contract DE-AC07-05ID14517 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

Publisher Copyright:
Published 2018. This article is a U.S. Government work and is in the public domain in the USA.


  • Peridynamics
  • bond-associated deformation gradient
  • correspondence model
  • material instability
  • zero-energy modes

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering (all)
  • Applied Mathematics


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