Elastic field at a rugous interface of a bimaterial with surface effects

Kostyrko, Sergey A.; Grekov, Mikhail A.

doi:10.1016/j.engfracmech.2019.106507

Cited by 11 publications

(10 citation statements)

References 72 publications

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“…where Boundary perturbation approach. According to [40], the solution of the BVP (1)-(6), specifically the stress σ n and displacement u complex vectors, can be derived using Goursat-Kolosov complex potentials Φ j and Υ j :…”

Section: Fig 1 a Model Of Bimaterials With Slightly Perturbated Intementioning

confidence: 99%

“…However, it is impossible to do this in the case of curved boundary as ζ = ζ. For this purpose, we use the BPM which has been applied recently in several publications to simplify BVP problems associated with complicated geometry and allowed to derive the analytic approximations of considered solutions [7][8][9][10][11][39][40][41].…”

Section: Fig 1 a Model Of Bimaterials With Slightly Perturbated Intementioning

confidence: 99%

“…Employing BPM, we expand the functions Φ j , Υ j , and τ in power series in small parameter ε as it was done in [40]:…”

Section: Fig 1 a Model Of Bimaterials With Slightly Perturbated Intementioning

confidence: 99%

“…Finally, taking into account the procedure developed in [40], we come to the recurrent sequence of hypersingular integral equations in unknown functions τ (m) :…”

Section: Fig 1 a Model Of Bimaterials With Slightly Perturbated Intementioning

confidence: 99%

“…However, as it was mentioned above, it is very important to analyze the stress state around the surface topological defects to predict the material failure. For this purpose, the boundary perturbation method (BPM) has been used extensively [39][40][41]. It should be noted that only the linear approximation of the BPM was analysed in these works.…”

mentioning

confidence: 99%

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The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

Shuvalov¹,

Vakaeva²,

Shamsutdinov³

et al. 2020

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

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Based on the Gurtin-Murdoch surface/interface elasticity theory, the article investigates the effect of nonlinear terms in the boundary perturbation method on stress concentration near the curvilinear bimaterial interface taking into account plane strain conditions. The authors consider the 2D boundary value problem for the infinite two-component plane under uniaxial tension. The interface domain is assumed to be a negligibly thin layer with the elastic properties differing from those of the bulk materials. Using the boundary perturbation method, the authors determined a semi-analytical solution taking into account non-linear approximations. In order to verify this solution, the corresponding boundary value problem was solved using the finite element method where the interface layer is modelled by the truss elements. It was shown that the effect of the amplitude-to-wavelength ratio of surface undulation on the stress concentration is nonlinear. This should be taken into account even for small perturbations. It was also found that the convergence rate of the derived solution increases with an increase in the relative stiffness coefficient of the bimaterial system and, conversely, decreases with an increase of the amplitude-to-wavelength ratio.

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Section: Fig 1 a Model Of Bimaterials With Slightly Perturbated Intementioning

confidence: 99%

Section: Fig 1 a Model Of Bimaterials With Slightly Perturbated Intementioning

confidence: 99%

“…Employing BPM, we expand the functions Φ j , Υ j , and τ in power series in small parameter ε as it was done in [40]:…”

Section: Fig 1 a Model Of Bimaterials With Slightly Perturbated Intementioning

confidence: 99%

“…Finally, taking into account the procedure developed in [40], we come to the recurrent sequence of hypersingular integral equations in unknown functions τ (m) :…”

Section: Fig 1 a Model Of Bimaterials With Slightly Perturbated Intementioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

Shuvalov¹,

Vakaeva²,

Shamsutdinov³

et al. 2020

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

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Coupled effect of curved surface and interface on stress state of wrinkled thin film coating at the nanoscale

2021

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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.

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Interaction of Misfit Dislocations with Perturbated Surface in Epitaxial Thin Film

Kostyrko

Grekov

Kitamura

2022

Lecture Notes in Control and Information Sciences - Proceedings

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Elastic field at a rugous interface of a bimaterial with surface effects

Cited by 11 publications

References 72 publications

The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

Coupled effect of curved surface and interface on stress state of wrinkled thin film coating at the nanoscale

Interaction of Misfit Dislocations with Perturbated Surface in Epitaxial Thin Film

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