Stress field around cylindrical nanopore by various models of surface elasticity

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Stress field around cylindrical nanopore by various models of surface elasticity. / Grekov, M.A.; Vakaeva, A.B.; Muller, W.H.

In: Continuum Mechanics and Thermodynamics, Vol. 35, No. 1, 01.2023, p. 231–243.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{04d2282a372d4175a9e4fd7d36e4e6f6,

title = "Stress field around cylindrical nanopore by various models of surface elasticity",

abstract = "Surface elasticity models including the Gurtin–Murdoch theory within the framework of continuummechanics are analyzed and applied to the 2-D boundary value problem of a circular cylindrical nanopore beingin an elastic body under remote loading. A brief overview of these models and their various applications isprovided in the paper. Assuming that the surface of the nanopore is free from an external load and incorporatingsurface stresses, the general boundary equation is formulated in terms of the unknown complex displacement.It is shown that the boundary equation of each model is a particular case of the general one. The solution ofthe problem in the general case including all models leads to the singular integro-differential equation which is explicitly evaluated. The final solution is presented for the stress field by means of elementary functions. The effect of each model on the stress field arising around the nanopore due to uniaxial remote loading is numerically investigated. It is disclosed that some models display both the great deviations and qualitative differences from the Gurtin–Murdoch model.",

keywords = "Circular cylindrical nanopore, Gurtin–Murdoch theory, Stress field, Surface elasticity models",

author = "M.A. Grekov and A.B. Vakaeva and W.H. Muller",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2023",

month = jan,

doi = "10.1007/s00161-022-01168-7",

language = "English",

volume = "35",

pages = "231–243",

journal = "Continuum Mechanics and Thermodynamics",

issn = "0935-1175",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - Stress field around cylindrical nanopore by various models of surface elasticity

AU - Grekov, M.A.

AU - Vakaeva, A.B.

AU - Muller, W.H.

PY - 2023/1

Y1 - 2023/1

N2 - Surface elasticity models including the Gurtin–Murdoch theory within the framework of continuummechanics are analyzed and applied to the 2-D boundary value problem of a circular cylindrical nanopore beingin an elastic body under remote loading. A brief overview of these models and their various applications isprovided in the paper. Assuming that the surface of the nanopore is free from an external load and incorporatingsurface stresses, the general boundary equation is formulated in terms of the unknown complex displacement.It is shown that the boundary equation of each model is a particular case of the general one. The solution ofthe problem in the general case including all models leads to the singular integro-differential equation which is explicitly evaluated. The final solution is presented for the stress field by means of elementary functions. The effect of each model on the stress field arising around the nanopore due to uniaxial remote loading is numerically investigated. It is disclosed that some models display both the great deviations and qualitative differences from the Gurtin–Murdoch model.

AB - Surface elasticity models including the Gurtin–Murdoch theory within the framework of continuummechanics are analyzed and applied to the 2-D boundary value problem of a circular cylindrical nanopore beingin an elastic body under remote loading. A brief overview of these models and their various applications isprovided in the paper. Assuming that the surface of the nanopore is free from an external load and incorporatingsurface stresses, the general boundary equation is formulated in terms of the unknown complex displacement.It is shown that the boundary equation of each model is a particular case of the general one. The solution ofthe problem in the general case including all models leads to the singular integro-differential equation which is explicitly evaluated. The final solution is presented for the stress field by means of elementary functions. The effect of each model on the stress field arising around the nanopore due to uniaxial remote loading is numerically investigated. It is disclosed that some models display both the great deviations and qualitative differences from the Gurtin–Murdoch model.

KW - Circular cylindrical nanopore

KW - Gurtin–Murdoch theory

KW - Stress field

KW - Surface elasticity models

UR - http://www.scopus.com/inward/record.url?scp=85144095612&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/aa3e910e-2644-334b-9001-47f4c7564a5f/

U2 - 10.1007/s00161-022-01168-7

DO - 10.1007/s00161-022-01168-7

M3 - Article

VL - 35

SP - 231

EP - 243

JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

IS - 1

ER -

ID: 101236406