The role of adhesion in contact mechanics

Abstract

<jats:p>Adhesive (e.g. van der Waals) forces were not generally taken into account in contact mechanics until 1971, when Johnson, Kendall and Roberts (JKR) generalized Hertz’ solution for an elastic sphere using an energetic argument which we now recognize to be analogous to that used in linear elastic fracture mechanics. A significant result is that the load–displacement relation exhibits instabilities in which approaching bodies ‘jump in’ to contact, whereas separated bodies ‘jump out’ at a tensile ‘pull-off force’. The JKR approach has since been widely used in other geometries, but at small length scales or for stiffer materials it is found to be less accurate. In conformal contact problems, other instabilities can occur, characterized by the development of regular patterns of regions of large and small traction. All these instabilities result in differences between loading and unloading curves and consequent hysteretic energy losses. Adhesive contact mechanics has become increasingly important in recent years with the focus on soft materials (which generally permit larger areas of the interacting surfaces to come within the range of adhesive forces), nano-devices and the analysis of bio-systems. Applications are found in nature, such as insect attachment forces, in nano-manufacturing, and more generally in industrial systems involving rubber or polymer contacts. In this paper, we review the strengths and limitations of various methods for analysing contact problems involving adhesive tractions, with particular reference to the effect of the inevitable roughness of the contacting surfaces.</jats:p>

A semi-analytical method for analys of contact interaction between structural elements along aligned surfaces

“…Among them, the lack of a universal mechanism for taking into consideration different factors, in particular, the properties of materials in the intermediate layers between the bodies in contact. Studies [17][18][19] address the models of properties of the rough surfaces of contacting bodies, taking into consideration their wave-like shapes. Papers [20][21][22] describe the effect of a geometric shape of surfaces and the distribution of a material's properties on the contact interaction between elastic bodies.…”

Elliptical adhesive contact under biaxial stretching

“…Contact mechanics with adhesion of elastic bodies has been applied to cell adhesion, originally in the form of the simple Johnson-Kendall-Roberts (JKR) theory [1], where it was shown that, unless it is disrupted, the cytoskeleton provides cells with a three-dimensional structure that is appropriate for JKR theory to be valid [2]; this includes that the material is relatively soft for the contact size to be regulated by what is essentially a Griffith energy criterion (for a recent review of adhesion, see [3]).…”

“…10a,b shows the plots of the relative contact areaà = π 1 − e 2ã2 versus the dimensional measure of stretch in the strain-and stress-controlled cases, respectively. (v) Axisymmetric loadingRecall[3] that the JKR-type models of adhesion are applicable for relatively large values of the Tabor parameter[39] μ T = RGwhere z 0 is the range of attraction of adhesive forces.…”

On Adhesive Theories in Multilayered Interfaces, With Particular Regard to "Surface Force Apparatus" Geometry

“…In a recent paper [1], the role of adhesion in contact mechanics has been reviewed starting in particular from the fundamental contribution of Johnson, Kendall and Roberts (JKR) [2], who generalized Hertz' theory to include van der Waals forces described as infinitely short range forces, so that a "contact area" can still be defined, which includes both compressive and tensile stresses. JKR theory has been confirmed in a number of investigations: in principle it should hold only for soft materials and large sphere radius, but in practice for a single, smooth asperity, it holds approximately even for dimensions appropriate to the Atomic Force Microscope (AFM), or the Surface Force Apparatus (SFA).…”