Local near-surface buckling of a system consisting of an elastic (viscoelastic) substrate, a viscoelastic (elastic) bond layer, and an elastic (viscoelastic) covering layer
- 23 Downloads
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.
Keywordslocal near-surface buckling stability viscoelastic layer nanocomposite curved layer critical time initial local imperfection
Unable to display preview. Download preview PDF.
- 2.A. N. Guz’, Fracture Mechanics of Composites in Compression [in Russian], Naukova Dumka, Kiev (1990).Google Scholar
- 3.S. D. Akbarov and A. N. Guz’, Mechanics of Curved Composites, Kluwer Academic Publisher, Dortrecht-Boston-London (2000).Google Scholar
- 10.M. A. Biot, Mechanics of Incremental Deformations, Wiley, New York (1965).Google Scholar
- 11.A. N. Guz’, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).Google Scholar
- 12.N. J. Hoff, “A surway of the theories of creep buckling,” in: Proc. Third US National Congress of the Applied Mechanics, ASME, New York (1958).Google Scholar
- 14.R. A. Schapery, “Approximate method of transform inversion for viscoelastic stress analysis,” Proc. US Nat. Congr. Appl. Mech., ASME, 4, 1075–1085 (1966).Google Scholar
- 15.Yu. N. Rabotnov, Elements of Hereditary Mechanics of Solid Bodies [in Russian], Nauka, Moscow (1977)Google Scholar
- 16.A. Cilli, Fracture of the Uni-Directed Fiber-Layered Composites in Compression, PhD Thesis, The Yildiz Technical University, Istanbul (1998).Google Scholar