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The theory of ideal adhesion interactions

Belov PA, Lurie SA

#### Abstract:

We used “kinematic” variational principle of construction of models of continuous media with a generalized kinematics. The new element in this approach is the account of the links between distortion and movement not only in the volume of the medium, but also on the surface. This leads to the appearance in the Lagrangian of the theory of the surface density of the potential energy in its structure similar to the bulk density of the potential energy for a transversely isotropic medium in a direction normal to the surface. Shows the variational formulation, obtained by the Euler equations and the corresponding range boundary value problems. Differential equilibrium equations coincide with the equations of the classical theory of elasticity, but “static” boundary conditions contain additional terms with second derivatives of the displacement in the tangential direction to the surface. By analogy with the equilibrium equations in the additional terms of body volume are treated as flat divergence adhesion stress. It is shown that formulated the theory describes the effect of the Laplace capillary pressure as a consequence of its strict. The theory predicts the existence of analogous effects in the shear stress. Formulated the theory of thin films with adhesion faces, which gives an explanation of the effect of increasing the hardness of very thin films with decreasing film thickness. The theory also provides an explanation for the abnormal stiffness properties of nanotubes and nanoplates as a result of a significant impact on their adhesion film surface. Investigation of dynamic equations for the classical media with the adhesive properties of surfaces possible to predict the existence of a spectrum of surface waves caused by the existence of the adhesive properties of the surface. An explanation of the effect of capillary ripples as the resonant formation of standing W-waves (one of the types of surface adhesion of the predicted waves). Similar effects occur for other types of surface waves adhesive.

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