@article{363ef7deb2f24de7a37abd96c0d555e2,
title = "On stress singularity near the tip of a crack with surface stresses",
abstract = "In the framework of the simplified linear Gurtin–Murdoch surface elasticity we discuss a singularity of stresses and displacements in the vicinity of a mode III crack. We show that inhomogeneity in surface elastic properties may significantly affect the solution and to change the order of singularity. We also demonstrate that implicitly or explicitly assumed symmetry of the problem may also lead to changes in solutions. Considering various loading and symmetry conditions we show that the stresses may have logarithmic or square root singularity or be bounded in the vicinity of a crack tip",
keywords = "mode III crack, surface stresses, nonhomogeneous surface properties, Wiener-Hopf equation, Mode III crack, Wiener–Hopf equation, Nonhomogeneous surface properties, Surface stresses",
author = "Nikolai Gorbushin and Eremeyev, {Victor A.} and Gennady Mishuris",
note = "Funding Information: V.A.E. acknowledges the support by grant 14.Z50.31.0036 awarded to R. E. Alekseev Nizhny Novgorod Technical University by Department of Education and Science of the Russian Federation. GM acknowledges financial support from the ERC Advanced Grant “Instabilities and nonlocal multiscale modelling of materials”, ERC-2013-ADG-340561-INSTABILITIES. He is also thankful to the Royal Society for the Wolfson Research Merit Award and the Isaac Newton Institute for Mathematical Sciences (INI) for Simon{\textquoteright}s Fellowship. NG and GM would like to thank INI, Cambridge, for support (through the EPSRC grant no EP/R014604/1 ) and hospitality during the programme “Bringing pure and applied analysis together via the Wiener-Hopf technique, its generalisations and applications” where work on this paper was completed. NG acknowledges the support of the French Agence Nationale de la Recherche (ANR) under reference ANR-17-CE08-0047-02 . Publisher Copyright: {\textcopyright} 2019 The Authors",
year = "2020",
month = jan,
day = "1",
doi = "10.1016/j.ijengsci.2019.103183",
language = "English",
volume = "146",
journal = "International Journal of Engineering Science",
issn = "0020-7225",
publisher = "Elsevier",
}