Taut contact hyperbolas on three-manifolds

In this paper, we introduce the notion of taut contact hyperbola on three-manifolds. It is the hyperbolic analogue of the taut contact circle notion introduced by Geiges and Gonzalo (Invent. Math., 121: 147–209, 1995), (J. Differ. Geom., 46: 236–286, 1997). Then, we characterize and study this notion, exhibiting several examples, and emphasizing differences and analogies between taut contact hyperbolas and taut contact circles. Moreover, we show that taut contact hyperbolas are related to some classic notions existing in the literature. In particular, it is related to the notion of conformally Anosov flow, to the critical point condition for the Chern–Hamilton energy functional and to the generalized Finsler structures introduced by R. Bryant. Moreover, taut contact hyperbolas are related to the bi-contact metric structures introduced in D. Perrone (Ann. Global Anal. Geom., 52: 213–235, 2017).

Contact Model for Incompressible Neo-Hookean Materials Under Finite Spherical Indentation

In this paper, a contact model is proposed to predict the contact response of an incompressible neo-Hookean half-space under finite spherical indentations. The axisymmetric finite element (FE) model is created to simulate the contact behaviors. Inspired by the numerical results, the radius of the contact circle is derived. The contact force is then obtained by modifying the radius of the contact circle of the Hertz model. The format of the distribution of the contact pressure is also developed according to the Hertz model. A parameter, determined by fitting the numerical results, is introduced to characterize the effect of the indentation depth on the shape of the distribution function of the contact pressure. The newly proposed contact model is numerically validated to predict well the contact behaviors, including the contact force, the radius of the contact circle, and the distribution of the contact pressure, for the incompressible neo-Hookean half-space under spherical indentation up to the indenter radius. However, the Hertz model is verified to offer acceptable predictions of the contact behaviors for the incompressible neo-Hookean materials within the indentation depth of 0.1 times of the indenter radius.

An analytical theory for the capillary bridge force between spheres

An analytical theory has been developed for properties of a steady, axisymmetric liquid–gas capillary bridge that is present between two identical, perfectly wettable, rigid spheres. In this theory the meridional profile of the capillary bridge surface is represented by a part of an ellipse. Parameters in this geometrical description are determined from the boundary conditions at the three-phase contact circle at the sphere and at the neck (i.e. in the middle between the two spheres) and by the condition that the mean curvature be equal at the three-phase contact circle and at the neck. Thus, the current theory takes into account properties of the governing Young–Laplace equation, contrary to the often-used toroidal approximation. Expressions have been developed analytically that give the geometrical parameters of the elliptical meridional profile as a function of the capillary bridge volume and the separation between the spheres. A rupture criterion has been obtained analytically that provides the maximum separation between the spheres as a function of the capillary bridge volume. This rupture criterion agrees well with a rupture criterion from the literature that is based on many numerical solutions of the Young–Laplace equation. An expression has been formulated analytically for the capillary force as a function of the capillary bridge volume and the separation between the spheres. The theoretical predictions for the capillary force agree well with the capillary forces obtained from the numerical solutions of the Young–Laplace equation and with those according to a comprehensive fit from the literature (that is based on many numerical solutions of the Young–Laplace equation), especially for smaller capillary bridge volumes.

Prediction Model for Bubble Contact Circle Diameter on Heating Wall

Phenomenal and theoretical analysis about the evolution of bubble contact circle diameter during bubble growing is presented in current paper; and it is found that bubble contact diameter is dependent on bubble growth rate and bubble radius strongly. By analyzing experimental data from open literature, the relation between dimensionless bubble contact diameter, kw, and dimensionless bubble growth time, t+, is obtained; based on this, a model relative to dimensionless bubble growth rate, dR+/dt+, and dimensionless bubble radius, R+, is proposed for prediction of bubble contact diameter. With proper values for coefficients, aw and nw, this model can well predict experimental data of bubble circle contact diameter in published literatures, with an error within ±20%.

On the Role of Contact Stresses in Frictional Damping of Mechanical Oscillation

Damping of spinning oscillations of a steel ball on an elastic base has been investigated. These oscillations are excited by the elastic force of a spring and damped by spinning friction. Oscillograms show the decrease of the amplitude to zero and of the period to a constant value, which can be calculated from the “elastic compliance of contact” and the compliance of the spring. Three different phases of oscillations, corresponding to three different kinds of damping can be distinguished. These are caused by: (a) Sliding over the entire contact area; (b) slips over the annular areas, while the internal stuck circle increases with decreasing amplitude; (c) oscillations of the ball, already stuck to the base by adhesion forces over the entire contact circle. The damping arises now from internal damping of base material. The periods of oscillations in two cases have been calculated theoretically.

Compliance Under a Small Torsional Couple of an Elastic Plate Pressed Between Two Identical Elastic Spheres

The object of the analysis is to calculate the surface shear traction and the torsional compliance of an elastic system comprising a plate pressed between identical spheres. The problem is formulated in terms of an integral equation which is solved numerically. The parameters are the plate thickness and ratio of shear moduli. Solutions are obtained for all except extremely thin plates, for which a previous approximate solution is shown to be valid. The contact stress distribution is always close to the well-known distribution appropriate to the half-space, with a singularity at the edge of the contact circle, unless the plate is simultaneously thin and flexible. A thin flexible plate confines the singularity to a very small region at the edge of the contact circle, the stress elsewhere being essentially proportional to radius. The torsional compliance predicted by the analysis agrees well with experiment.