Instability of an elastic film on a viscous layer

A flat, compressed elastic film on a viscous layer is unstable. The film can form wrinkles to reduce the elastic energy. In this paper, we are interested in the two-dimensional models for thin films bonded to a viscous layer and in particular we focus on generic instabilities evidenced in this context by Suo and coworkers [Huang, Z., Hong, W., Suo, Z., 2005. Non linear analyses of wrinkles in a film bonded to a compliant substrate. J. Mech. Phys. Solids 53, 2101–2118; Lo, Y.H., 1991. New approach to grow pseudomorphic structures over the critical thickness. Appl. Phys. Lett. 59, 2311–2320]. We present a rigorous linear perturbation analysis for anisotropic materials, that allows the prediction of both the orientation of the corrugations of the thin film, and the wavelength that maximize the growth velocity. Finally, we compare our theoretical estimates to experimental results for a In_0.65Ga_0.35As alloy constraint to InP.     

Wrinkling of a charged elastic film on a viscous layer

A thin metallic film deposited on a compliant polymeric substrate begins to wrinkle under compression induced in curing process and afterwards cooling of the system. The wrinkle mode depends upon the thin film elasticity, thickness, compressive strain, as well as mechanical properties of the compliant substrate. This paper presents a simple model to study the modulation of the wrinkle mode of thin metallic films bonded on viscous layers in external electric field. During the procedure, linear perturbation analysis was performed for determining the characteristic relation that governs the evolution of the plane-strain wrinkle of the thin films under varying conditions, i.e., the maximally unstable wrinkle mode as a function of the film surface charge, film elasticity and thickness, misfit strain, as well as thickness and viscosity of the viscous layer. It shows that, in proper electric field, thin film may wrinkle subjected to either compression or tension. Therefore, external electric field can be employed to modulate the wrinkle mode of thin films. The present results can be used as the theoretical basis for wrinkling analysis and mode modulation in surface metallic coatings, drying adhesives and paints, and microelectromechanical systems (MEMS), etc.     

Buckling and postbuckling of a compressed thin film bonded on a soft elastic layer: a three-dimensional analysis

The wrinkling of a stiff thin film bonded on a soft elastic layer and subjected to an applied or residual compressive stress is investigated in the present paper. A three-dimensional theoretical model is presented to predict the buckling and postbuckling behavior of the film. We obtained the analytical solutions for the critical buckling condition and the postbuckling morphology of the film. The effects of the thicknesses and elastic properties of the film and the soft layer on the characteristic wrinkling wavelength are examined. It is found that the critical wrinkling condition of the thin film is sensitive to the compressibility and thickness of the soft layer, and its wrinkling amplitude depends on the magnitude of the applied or residual in-plane stress. The bonding condition between the soft layer and the rigid substrate has a considerable influence on the buckling of the thin film, and the relative sliding at the interface tends to destabilize the system.     

Waves in a viscous layer of fluid on an elastic half-space

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 4, pp. 3–7, April, 1990.     

Interaction of an elastic boundary with a viscous sublayer of a turbulent boundary layer

The boundary region of a turbulent boundary layer contributes greatly to the drag. Intense turbulence is generated in this region. Below we investigate the interaction of an elastic boundary with a viscous sublayer for a decrease in the Reynolds stresses, and for a corresponding decrease in the drag. It does not seem possible to investigate the general case. Therefore, the problem is solved within the framework of the limitations made by Sternberg [1] for the theory of a viscous sublayer in a turbulent flow near a solid smooth wall.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 58–62, May–June, 1971.The authors thanks G. S. Migirenko for advice and remarks given during a discussion of the work.     

Instability of a film of viscous liquid under the influence of an adjacent gas flow

A study is made of the instability of a film of viscous liquid adjacent to a gas flow. Despite a number of investigations, there is no unified theory of this problem capable of explaining the experimental results of different authors. The present paper gives a solution of the problem that is valid for a large class of flows of liquid films in the case of laminar and turbulent flow of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 28–36, March–April, 1979.     

Instability of long-wave viscous flows

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 30–35, Jul–August, 1990.     

Dynamics of interaction between a squeezed layer of a viscous incompressible fluid and an elastic three-layer plate

We study the hydrodynamic response of a thin layer of a viscous incompressible fluid squeezed between impermeable walls. We consider the distribution of pressure and force dynamic characteristics of the fluid layer in the case of forced flows along the gap between a vibration generator (which is a rigid plane) exhibiting harmonic vibrations and a stator (which is an elastic freely supported three-layer plate). The inertial forces of the viscous fluid motion and the stator elastic properties are taken into account. The amplitude and phase frequency characteristics of the elastic three-layer plate are found from the solution of the plane problem.     

Instability of a moving plane-parallel layer

A study is made of infinitely small perturbations of a moving plane-parallel layer. It is shown that, in distinction from an isolated tangential discontinuity, a layer is unstable with any given values of the projection of the velocity of the layer on the wave vector of the perturbation. The instability of an isolated tangential discontinuity has been repeatedly investigated in detail (see, for example, [1–4]). The instability of a moving layer has remained almost unanalyzed. It is of importance to make such an analysis, the more so since the results for a layer differ qualitatively from the results for an isolated tangential discontinuity.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 11–14, May–June, 1972.     

Buckling modes of a compressed plate on an elastic substrate

The buckling modes of a homogeneously compressed elastic plate on a soft elastic substrate are studied. The critical compression is uniquely determined by the bifurcation equation, but this compression is associated with a wide set of buckling modes. It was proved that any solution of the Helmholtz equation satisfies the bifurcation equation. At the same time, in microelectronics, it is required to know which buckling mode is realized. Experimental and theoretical investigations show that the chessboard-like buckling mode should be expected. In what follows, this problem is discussed theoretically. The expected buckling mode can be found by analyzing the energy of the initial postcritical deformation, and the desired mode is determined from the condition of its minimum. The analytic expression of this energy is obtained. Its minimization results in the chessboard-like buckling mode.     

Instability of elastic bodies

The study of the equilibrium of systems constitutes an important chapter of applied mechanics. Since Euler’s works on beam buckling, in 1774, many eminent specialists studied the problem of the elastic instability of structures.An examination of many works published in this field shows a large number of approaches or criteria adopted by various authors. The objective of this study is to show through a classical example the link between the different approaches to provide a multi-level basis and to propose a valid global approach for conservative as well as nonconservative systems.     

Instability of a liquid layer under periodic influence: Falling film in an alternating electric field

The linear analysis of stability of a plane-parallel time-periodic flow is carried out. The numerical method which makes it possible to reduce the spectral problem for the time-dependent Orr–Sommerfeld equation to an algebraic eigenvalue problem is used. The film of viscous conducting liquid which flows down a vertical wall in the normal electric field is considered and parametric resonances are revealed.     

Instability of the boundary layer on a curved surface

The excitation of instability of the boundary layer on a curved surface in the limit R (R is the Reynolds number) is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 176–179, January–February, 1990.I am grateful to O. S. Ryzhov for his interest in the work.     

Instability of a three-dimensional supersonic boundary layer

This study was conducted with financial support from the Russian Fund for Basic Research (Grant No. 94-01-000497).     

Motion of a free axisymmetric viscous liquid film

Axisymmetric free-film flows are encountered in connection with the atomization of liquids and the collision of jets [1, 2]. In [3] steady motion with transverse symmetry is examined and its inviscid instability is studied. Here, steady flow with an arbitrary velocity profile is investigated numerically by the collocation method. The study of the stability of the steady flow under the assumption of local plane-parallelism leads to the formulation of a sixth-order eigenvalue problem which is solved numerically. The existence of unstable disturbances of two types is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 23–29, July–August, 1990.