Bond-associated deformation gradients for peridynamic correspondence model

Research output: Contribution to journalArticlepeer-review

54 Scopus citations

Abstract

Non-ordinary state-based peridynamic correspondence material model is known to have issues with material instability, i.e. the existence of zero-energy modes, due to non-unique mapping between deformation states and force states via the conventional peridynamic deformation gradient. In this paper, an alternative approach in which the deformation gradient hence force state are computed specifically for each individual bond is proposed to eliminate the material instability. Bond-associated deformation gradient is calculated based on deformation states within an individual bond's proximity, termed here as the bond-associated family, rather than the whole family. This bond-associated deformation gradient can better represents the force state of each individual bond from the deformation states within its proximity, and hence inherently resolves issues of material instability in the conventional correspondence material model. Parametric study on bond-associated horizon size indicates that the optimal size should be no less than the material point's horizon size but smaller than two times of that value. Comparisons against reference solutions using finite element method establish the validity and accuracy of the proposed formulation.

Original languageEnglish
Pages (from-to)34-41
Number of pages8
JournalMechanics Research Communications
Volume90
DOIs
StatePublished - Jun 2018

Bibliographical note

Funding Information:
Work 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 No. 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.

Funding Information:
Work 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 No. 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:
© 2018 Elsevier Ltd

Keywords

  • Correspondence material model
  • Deformation gradient
  • Material Instability
  • Peridynamics
  • State-based peridynamics
  • Zero-energy modes

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Materials Science (all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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