A dynamic hybrid local/nonlocal continuum model for wave propagation

Fei Han, Shankun Liu, Gilles Lubineau*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


In this work, we develop a dynamic hybrid local/nonlocal continuum model to study wave propagations in a linear elastic solid. The developed hybrid model couples, in the dynamic regime, a classical continuum mechanics model with a bond-based peridynamic model using the Morphing coupling method that introduced in a previous study (Lubineau et al., J Mech Phys Solids 60(6):1088–1102, 2012). The classical continuum mechanical model is known as a local continuum model, while the peridynamic model is known as a nonlocal continuum model. This dynamic hybrid model aims to introduce the nonlocal model into the key structural domain, in which the dispersions or crack nucleations may occur due to flaws, while applying the local model to the rest of the structural domain. Both the local and nonlocal continuum domains are overlapped in the coupled subdomain. We study the speeds and angular frequencies of the plane waves, with small and large wavenumbers obtained by the hybrid model and compare them to purely local and purely nonlocal solutions. The error of the hybrid model is discussed by analyzing the ghost forces, and the work done by the ghost forces is considered equivalent to the energy of spurious reflections. One- and two-dimensional numerical examples illustrate the validity and accuracy of the proposed approach. We show that this dynamic hybrid local/nonlocal continuum model can be successfully applied to simulate wave propagations and crack nucleations induced by waves.

Original languageEnglish (US)
Pages (from-to)385-407
Number of pages23
JournalComputational Mechanics
Issue number1
StatePublished - Jan 2021

Bibliographical note

Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.


  • Continuum mechanics
  • Fracture
  • Hybrid model
  • Morphing coupling method
  • Peridynamics
  • Wave dispersion

ASJC Scopus subject areas

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


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