Local near-surface buckling of a system consisting of an elastic (viscoelastic) substrate,a viscoelastic (elastic) bond layer,and an elastic (viscoelastic) covering layer |
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Authors: | E A Aliyev |
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Institution: | (1) Faculty of Arts and Sciences, Department of Physics, Esentepe Campus, Sakarya University, Sakarya, Turkey |
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Abstract: | Within the framework of a piecewise homogenous body model and with the use of a three-dimensional linearized theory of stability
(TLTS), the local near-surface buckling of a material system consisting of a viscoelastic (elastic) half-plane, an elastic
(viscoelastic) bond layer, and a viscoelastic (elastic) covering layer is investigated. A plane-strain state is considered,
and it is assumed that the near-surface buckling instability is caused by the evolution of a local initial curving (imperfection)
of the elastic layer with time or with an external compressive force at fixed instants of time. The equations of TLTS are
obtained from the three-dimensional geometrically nonlinear equations of the theory of viscoelasticity by using the boundary-form
perturbation technique. A method for solving the problems considered by employing the Laplace and Fourier transformations
is developed. It is supposed that the aforementioned elastic layer has an insignificant initial local imperfection, and the
stability is lost if this imperfection starts to grow infinitely. Numerical results on the critical compressive force and
the critical time are presented. The influence of rheological parameters of the viscoelastic materials on the critical time
is investigated. The viscoelasticity of the materials is described by the Rabotnov fractional-exponential operator.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 771–788, November–December, 2007. |
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Keywords: | local near-surface buckling stability viscoelastic layer nanocomposite curved layer critical time initial local imperfection |
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