Modelling of viscoelastic materials using non-ordinary state-based peridynamics

Yakubu Kasimu Galadima, Selda Oterkus, Erkan Oterkus, Islam Amin, Abdel-Hameed El-Aassar, Hosam Shawky

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
38 Downloads (Pure)

Abstract

This paper proposes a framework for implementing viscoelastic constitutive model from the classical continuum mechanics (CCM) theory within non-ordinary state-based peridynamics (NOSBPD). The motivation stems from the inadequacy of CCM to model very complex material behaviours such as initiation and propagation of cracks and nonlocal behaviour due to size effects. The proposed formulation leverages on the constitutive correspondence between NOSBPD and CCM to incorporate a CCM viscoelastic constitutive model based on hereditary integral into NOSBPD. The combination of hereditary constitutive model and NOSBPD effectively makes this formulation a nonlocal time-space viscoelastic framework where temporal nonlocality is incorporated by a hereditary viscoelastic model which stipulates that the behaviour of a material at any point in time depends on both the present action and the complete history of previous actions on the material, and spatial nonlocality on the other hand is incorporated via the nonlocal mechanism provided by the NOSBPD. For model validation, three benchmark problems were solved using the proposed framework. Results obtained were compared with results from analytical solution and solutions from referenced literature. In addition, parametric study was conducted to determine the influence of nonlocality on numerical prediction. Conclusions drawn from the validation studies presented are that the proposed framework is able to predict viscoelastic responses that agree well with local macro models as well as nonlocal micromodels/nanomodels as reported in the literature.
Original languageEnglish
Pages (from-to)527-540
Number of pages14
JournalEngineering with Computers
Volume40
Issue number1
Early online date22 Mar 2023
DOIs
Publication statusPublished - Feb 2024

Keywords

  • peridynamics
  • viscoelasticity
  • non-ordinary state-based
  • nonlocal

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