A numerical study of JKR-type adhesive contact of ellipsoids

Approximate solution by Johnson and Greenwood (2005) for an adhesive contact of an ellipsoid and an elastic half-space is revisited numerically using the FFT-based Boundary Element Method. While for moderate values of the ratio of principal radii of the ellipsoid, R1/R2, predictions of the Johnson-Greenwood approximate theory are very good, they become increasingly inaccurate for large values of this parameter. On the basis of numerical simulations, we provide analytical approximations for the dependencies between load, approach and contact area and compare the exact shape of the contact area with the elliptical one assumed in the Johnson-Greenwood-theory

On the origin of the Fermi arc phenomena in the underdoped cuprates: signature of KT-type superconducting transition

We study the effect of thermal phase fluctuation on the electron spectral function $A(k,\omega)$ in a d-wave superconductor with Monte Carlo simulation. The phase degree of freedom is modeled by a XY-type model with build-in d-wave character. We find a ridge-like structure emerges abruptly on the underlying Fermi surface in $A(k,\omega=0)$ above the KT-transition temperature of the XY model. Such a ridge-like structure, which shares the same characters with the Fermi arc observed in the pseudogap phase of the underdoped cuprates, is found to be caused by the vortex-like phase fluctuation of the XY model.Comment: 5 page

INDENTATION OF FLAT-ENDED AND TAPERED INDENTERS WITH POLYGONAL CROSS-SECTIONS

Using the Boundary Element Method, we numerically study the indentation of prismatic and tapered indenters with polygonal cross-sections. The contact stiffness of punches with flat bases in the form of a triangle and a square as well as a number of higher-order polygons is determined. In particular, the classical results of King (1987) for indenters with triangle and square base shapes are revised and more precise numerical results are provided. For tapered indenters, the equivalent transformed profile used in the Method of Dimensionality Reduction (MDR) is determined. It is shown that the MDR-transformed profile of polygon-based indenters with power function side is given by the power function with the same power; it differs from the 3D profile only by a constant coefficient. These coefficients are listed in the paper for various types of indenters, in particular for pyramidal and paraboloid ones. The determined MDR-transformed profiles can be used for study of other contact problems such as tangential contact, normal contact with elastomers, and, in an approximate way, to adhesive contacts

NORMAL LINE CONTACT OF FINITE-LENGTH CYLINDERS

In this paper, the normal contact problem between an elastic half-space and a cylindrical body with the axis parallel to the surface of the half-space is solved numerically by using the Boundary Element Method (BEM). The numerical solution is approximated with an analytical equation motivated by an existing asymptotic solution of the corresponding problem. The resulting empirical equation is validated by an extensive parameter study. Based on this solution, we calculate the equivalent MDR-profile, which reproduces the solution exactly in the framework of the Method of Dimensionality Reduction (MDR). This MDR-profile contains in a condensed and easy-to-use form all the necessary information about the found solution and can be exploited for the solution of other related problems (as contact with viscoelastic bodies, tangential contact problem, and adhesive contact problem.) The analytical approximation reproduces numerical results with high precision provided the ratio of length and radius of the cylinder are larger than 5. For thin disks (small length-to-radius ratio), the results are not exact but acceptable for engineering applications

Non-adhesive Contacts With Different Surface Tension Inside and Outside the Contact Area

In the past decade, the influence of surface tension on contact properties has attracted much attention, especially in the context of contact of very soft materials (such as gels) or contacts at the nanoscale. However, in the most current studies it is assumed that the tension of the surface inside and outside the contact area is the same. In practical terms, this means that the object considered is an elastic body “coated” with a tensed membrane. In real contacts, there is no reason why the surface tensions of the “free interface” and the “contact interface” should be equal. On the contrary, especially in contacts of soft bodies with hard solid indenters, one can anticipate that they are completely different. In the present article, we consider an elastic contact taking into account different surface tensions inside and outside the contact area. However, the considered contacts are still “non-adhesive.” This means that the three surface energies in play (two surface energies of both bodies outside the contact and the interface energy in the contact region) fulfill the criterion that the work of separation vanishes. A numerical model based on the Fast Fourier transform–assisted boundary element method is implemented and is illustrated with a few examples.TU Berlin, Open-Access-Mittel – 202