Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2020-2pp.207-217

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A.O. Vatulyan and K.L. Morozov, "Investigation of Delamination from an Elastic Base Using a Model with Two Coefficients of Subgrade Reaction," Mech. Solids. 55 (2), 207-217 (2020)
Year 2020 Volume 55 Number 2 Pages 207-217
DOI 10.3103/S002565442002017X
Title Investigation of Delamination from an Elastic Base Using a Model with Two Coefficients of Subgrade Reaction
Author(s) A.O. Vatulyan (South Federal University, Rostov-on-Don, 344090 Russia,
K.L. Morozov (South Federal University, Rostov-on-Don, 344090 Russia)
Abstract Currently, various structural components have coatings of different purposes that are multilayer or gradient structures. During operation these elements are often subjected to compressive loads, as a result of which sometimes the upper part of the coating is delaminated. To analyze this process, we use a simplified model of infinite structure, namely, a modified beam approximation that takes into account two coefficients of subgrade reaction similarly to the Pasternak model. The coating is subjected to compressive prestresses. Within the framework of the previously proposed model, delamination of the coating from the elastic base is investigated. We consider a simple case when the coefficients of subgrade reaction in the deamination zone are equal to zero. At the first stage, we conduct nondimensionalization of the model under study; obtain and study transcendental equation to find the critical load; prove the existence of a solution within some region of parameter variation; construct approximate formulas for the critical load; and indicate the correlation with the model parameters. The effect of the second coefficient of subgrade reaction on the critical load value is shown. At the second stage, based on the variational formulation, the problem of infinite coating is reduced to the problem on a finite beam with modified boundary conditions. The results obtained on the basis of a simplified model are compared with a numerical solution of the transcendental equation obtained at the first stage. At the final third stage, the problem on the supercritical behavior of the coating is investigated by minimizing the non-quadratic potential energy functional. Using the Ritz method and setting power-exponential functions corresponding to an infinite coating as coordinate, a solution of the problem on supercritical deformation is constructed. A study of the solution depending on the coefficients of subgrade reaction is carried out.
Keywords coating delamination from an elastic base, transcendental equation, supercritical behavior, Ritz method
Received 25 October 2019Revised 11 November 2019Accepted 20 November 2019
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