Periodic Green functions for two-component medium with interface stresses at the planar interface

Research output

1 Citation (Scopus)

Abstract

The 2-D problem of elasticity for bimaterial with planar interface under the periodic set of point forces is considered at the nanoscale. Complex variable based technique and Gurtin-Murdoch model of surface elasticity, which leads to the hypersingular integral equation, are used. The solution of this equation and explicit formulas for stress field (Green functions) are derived in terms of Fourier series. The fundamental solutions obtained in the work can be used for applying the boundary integral equation method to an analysis of defects such as cracks and inhomogeneities, periodically distributed at the nanometer distances from the interface.
Original languageEnglish
Pages (from-to)070014-1–070014-6
Number of pages6
JournalAIP Conference Proceedings
Volume1959
Publication statusPublished - 2018

Scopus subject areas

  • Mathematics(all)

Cite this

@article{3495c0fadec74a13bacc2633979d87c8,
title = "Periodic Green functions for two-component medium with interface stresses at the planar interface",
abstract = "The 2-D problem of elasticity for bimaterial with planar interface under the periodic set of point forces is considered at the nanoscale. Complex variable based technique and Gurtin-Murdoch model of surface elasticity, which leads to the hypersingular integral equation, are used. The solution of this equation and explicit formulas for stress field (Green functions) are derived in terms of Fourier series. The fundamental solutions obtained in the work can be used for applying the boundary integral equation method to an analysis of defects such as cracks and inhomogeneities, periodically distributed at the nanometer distances from the interface.",
author = "{Grekov M.A.} and {Sergeeva T.S.}",
year = "2018",
language = "English",
volume = "1959",
pages = "070014--1–070014--6",
journal = "AIP Conference Proceedings",
issn = "0094-243X",
publisher = "American Institute of Physics",

}

TY - JOUR

T1 - Periodic Green functions for two-component medium with interface stresses at the planar interface

AU - Grekov M.A., null

AU - Sergeeva T.S., null

PY - 2018

Y1 - 2018

N2 - The 2-D problem of elasticity for bimaterial with planar interface under the periodic set of point forces is considered at the nanoscale. Complex variable based technique and Gurtin-Murdoch model of surface elasticity, which leads to the hypersingular integral equation, are used. The solution of this equation and explicit formulas for stress field (Green functions) are derived in terms of Fourier series. The fundamental solutions obtained in the work can be used for applying the boundary integral equation method to an analysis of defects such as cracks and inhomogeneities, periodically distributed at the nanometer distances from the interface.

AB - The 2-D problem of elasticity for bimaterial with planar interface under the periodic set of point forces is considered at the nanoscale. Complex variable based technique and Gurtin-Murdoch model of surface elasticity, which leads to the hypersingular integral equation, are used. The solution of this equation and explicit formulas for stress field (Green functions) are derived in terms of Fourier series. The fundamental solutions obtained in the work can be used for applying the boundary integral equation method to an analysis of defects such as cracks and inhomogeneities, periodically distributed at the nanometer distances from the interface.

M3 - Article

VL - 1959

SP - 070014-1–070014-6

JO - AIP Conference Proceedings

JF - AIP Conference Proceedings

SN - 0094-243X

ER -