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Coupled effect of curved surface and interface on stress state of wrinkled thin film coating at the nanoscale
Author(s) -
Kostyrko Sergey,
Grekov Mikhail,
Altenbach Holm
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000202
Subject(s) - materials science , slipping , boundary value problem , elasticity (physics) , thin film , interphase , coating , surface stress , composite material , cauchy stress tensor , stiffness , plane stress , mechanics , finite element method , geometry , mathematics , mathematical analysis , nanotechnology , physics , surface energy , thermodynamics , biology , genetics
In this paper, we present the model of continuum mechanics for an analysis of the size‐dependent elastic state of the wrinkled thin film coating with the nanosized thickness. For this purpose, we formulate the two‐dimensional boundary value problem for the film‐on‐substrate system under plane strain conditions in terms of the complex variable. To analyse the effect of surface and interface elasticity, the surface and interphase domains are modelled as negligibly thin layers adhering to the bulk phases without slipping. The algorithm of deriving the expressions for the stress tensor components in the first‐order approximation of the boundary perturbation method is described. Based on this algorithm, the influence of the size of the wrinkles, film‐to‐substrate stiffness ratio and film thickness on the stress concentration in the film is examined.