4.7 Article

Stress field and effective elastic moduli of periodic spheroidal particle composite with Gurtin-Murdoch interface

Journal

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
Volume 132, Issue -, Pages 79-96

Publisher

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2018.08.001

Keywords

Nanocomposite; Spheroid; Elasticity; Interface stress; Multipole expansion; Effective stiffness

Funding

  1. Science and Technology Center in Ukraine (STCU) of Ukraine [6247-2]
  2. National Academy of Sciences (NAS) of Ukraine [6247-2]

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The periodic spheroidal particle nanocomposite with Gurtin-Murdoch type interface stress is considered. A complete semi-analytical solution to the unit cell model problem has been obtained by the multipole expansion method. To this end, the displacement perturbation field of the periodic array of inhomogeneities is expanded over a set of the periodic vector solutions of Lame equation in spheroidal basis. An accurate fulfilling the interface conditions reduces the model boundary value problem to an infinite set of linear algebraic equations for the multipole strengths. The obtained solution provides evaluation of the displacement, strain and stress in every point of the unit cell being, at the same time, the representative volume element of composite. Surface averaging the local strain and stress fields yields an exact expression of the effective stiffness tensor of composite in terms of the induced dipole moment of spheroidal inhomogeneity. Numerical examples demonstrate an accuracy and computational efficiency of the developed approach and shows significant combined effect of the geometry and elastic properties of interface on the elastic fields and macroscopic stiffness of periodic nanocomposite. (C) 2018 Elsevier Ltd. All rights reserved.

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