In-plane stress analysis of two nanoscale holes under surface tension

Studied in this paper is the surface tension-induced stress field around two nanoscale holes in an infinite, elastic matrix. The complex variable method is adopted to describe the assumed plane-strain deformation of the structure. The stress boundary conditions at the surfaces of the holes are formu...

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Bibliographic Details
Published in:Archive of applied mechanics (1991) Vol. 90; no. 6; pp. 1363 - 1372
Main Authors: Wang, Shuang, Yang, Hai-Bing, Gao, Cunfa, Chen, Zengtao
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2020
Springer Nature B.V
Subjects:
Approximation
Boundary conditions
Classical Mechanics
Complex variables
Conformal mapping
Engineering
Numerical methods
Original
Plane strain
Plane stress
Series expansion
Stress analysis
Stress distribution
Surface tension
Theoretical and Applied Mechanics
Two-hole problems
Surface tension
Nanoscale holes
Common shapes
Complex variable method
ISSN:0939-1533, 1432-0681
Online Access:Get full text
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Summary:Studied in this paper is the surface tension-induced stress field around two nanoscale holes in an infinite, elastic matrix. The complex variable method is adopted to describe the assumed plane-strain deformation of the structure. The stress boundary conditions at the surfaces of the holes are formulated via the integral-type Gurtin–Murdoch model. The stress field is finally obtained with the aid of conformal mapping and series expansion methods. Numerical examples are demonstrated for the case of one approximately triangular, smooth hole and one approximately square, smooth hole. A detailed discussion is carried out about the influence of the distance between the two holes on the stress field.
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ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-020-01672-9