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3-Dimensional Bond-Based Peridynamic Representative Volume Element Homogenization

Abstract

In this study, a 3-dimensional (3D) implementation of representative volume element homogenization using bond-based peridynamic formulation is presented. Periodic boundary condition is established by coupling the displacements of periodic point pairs. Homogenized (effective) material properties are obtained based on peridynamic displacement gradient tensor. The current approach is validated by considering a composite material without defects and comparing homogenized properties with results obtained from another homogenization approach. Next, the capability of the current approach is demonstrated by considering randomly generated cracks with arbitrary orientation and location. It can be concluded that the current approach can be an alternative approach to obtain 3-dimensional homogenized material properties for heterogeneous materials with defects.

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ACKNOWLEDGMENTS

The authors would like to dedicate this study to Professor Siegfried Schmauder for his 65th birthday.

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Correspondence to E. Oterkus.

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Xia, W., Oterkus, E. & Oterkus, S. 3-Dimensional Bond-Based Peridynamic Representative Volume Element Homogenization. Phys Mesomech 24, 541–547 (2021). https://doi.org/10.1134/S1029959921050052

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Keywords:

  • peridynamics
  • homogenization
  • periodic boundary condition
  • bond-based
  • 3D