Numerical Investigation of Effective Moduli of Porous Elastic Material with Surface Stresses for Various Structures of Porous Cells

  • A. V. NasedkinEmail author
  • A. S. Kornievsky
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 109)


The chapter deals with the model problem of finding the effective moduli of a nanoporous elastic material, in which the surface stresses are defined on the pore surface to reflect the size effect using the Gurtin–Murdoch model. One cell of a porous material in the form of a cube with one pore located in the center is considered. The objective of the study is to assess the influence of the pore shape and the magnitude of the scale factors on the effective moduli of the composite material. The homogenization problem is formulated within the framework of the effective moduli method, and to find its solution, the finite element method and the ANSYS software package are used. In the finite element model, the surface stresses are taken into account by membrane elements covering the pore surfaces and conformable with the finite element mesh of bulk elements. Numerical experiments carried out for pores of cubic and spherical shapes show the cumulative significant effect of pore geometry and scale factors on the effective elastic moduli.



This work was supported by the Russian Science Foundation (grant number 15–19-10008-P).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mathematics, Mechanics and Computer ScienceSouthern Federal UniversityRostov-on-DonRussia

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