Valentin L. Popov

Contact Mechanics and Friction

Objectives In the last decades, contact mechanics and tribology have expanded to qualitatively new fields of applications, which are at the forefront of global development trends of technology and society, in particular microand nanotechnology as well as biology and medicine. At the same time, tribology developed experimental methods, theoretical concepts and numerical tools allowing effectively mastering the seemingly complicated physics and mechanics of interconnections. The goal of the workshop is to review the recently established concepts, tools and research activities and to outline the most important tasks for the future.

Structural Design and Biomechanics of Friction-Based Releasable Attachment Devices in Insects

Abstract Design of attachment devices in insects varies enormously in relation to different functional loads. Many systems, located on different parts of the body, involve surfaces with particular frictional properties. Such systems evolved to attach parts of the body to each other, or to attach an insect to the substratum by providing fast and reversible attachment/detachment. Among these systems, there are some that deal with predefined surfaces, and others, in which one surface remains unpredictable. The first type of system occurs, for example, in wing-locking devices and head-arresting systems and is called probabilistic fasteners. The second type is mainly represented by insect attachment pads of two alternative designs: hairy and smooth. The relationship between surface patterns and/or mechanical properties of materials of contact pairs results in two main working principles of the frictional devices: mechanical interlocking, or maximization of the contact area. We give an overview of the functional design of two main groups of friction-based attachment devices in insects: probabilistic fasteners and attachment pads.

Method of dimensionality reduction in contact mechanics and friction

The Method of Dimensionality Reduction (MDR) is a method of calculation and simulation of contacts of elastic and viscoelastic bodies. It consists essentially of two simple steps: (a) substitution of the three-dimensional continuum by a uniquely defined one-dimensional linearly elastic or viscoelastic foundation (Winkler foundation) and (b) transformation of the three-dimensional profile of the contacting bodies by means of the MDR-transformation. As soon as these two steps are completed, the contact problem can be considered to be solved. For axial symmetric contacts, only a small calculation by hand is required which does not exceed elementary calculus and will not be a barrier for any practically-oriented engineer. Alternatively, the MDR can be implemented numerically, which is almost trivial due to the independence of the foundation elements. In spite of their simplicity, all the results are exact. The present paper is a short practical guide to the MDR.

Earthquakes and Friction

Tectonic plate dynamics can also be seen as a part of tribology. The Earth’s crust is composed of tectonic plates which slowly move relative to one another due to convection in the mantel. On a time scale of millions of years, these movements determine the structure of the Earth’s surface. On a small time scale, they are responsible for earthquakes. Frictional models have applications for describing the dynamics of individual faults as well as describing the Earth’s crust as a granular medium. Models for mechanisms of earthquakes are based on the fundamental observation that earthquakes do not arise as a result of a sudden formation and propagation of a new crack in the Earth’s crust, rather they take place as a result of a sudden sliding along an already existing faults.

Subsurface layer formation during sliding friction

Abstract Considering recent experimental studies and analysis of the literature, the authors substantiate the potential of physical mesomechanics for describing structural degradation of subsurface structures during friction and wear. Physical mesomechanics may be a useful approach for constructing a generalized hierarchical model that has its origin in vortical “shear+rotation” motion of mesovolumes resulting in formation of wear particles. The most important constituents of such a model are mechanical cyclic and thermal actions, both related to the interplay between the surface microirregularities, localization of strain and fragmentation of material at different scale levels.

Shear induced adhesion: Contact mechanics of biological spatula-like attachment devices

Most biological hairy adhesive systems of insects, arachnids, and reptiles, involved in locomotion, rely not on flat punches on their tips, but rather on spatulate structures. Several hypotheses have been previously proposed to explain the functional importance of this particular contact geometry: (1) enhancement of adaptability to the rough substrate; (2) contact formation by shear force rather than by normal load; (3) increase in total peeling line due to the use of an array of multiple spatulae; (4) contact breakage by peeling off. In the present paper, we used numerical approach to study dynamics of spatulate tips during contact formation on rough substrates. The model clearly demonstrates that the contact area increases under applied shear force, especially when spatulae are misaligned prior to the contact formation. Applied shear force has an optimum describing the situation when maximal contact is formed but no slip occurs. At such equilibrium, maximal adhesion can be generated. This principle manifests the crucial role of spatulate terminal elements in biological fibrillar adhesion.

Quasi-fluid nano-layers at the interface between rubbing bodies: simulations by movable cellular automata

Abstract Most of technical surfaces show roughness on different space scales. When pressed against each other, they initially come into contact only in small number of micro-contacts. Our aim was to study the processes occurring in a single micro-contact between two rubbing bodies. The solids were simulated in the frame of the method of movable cellular automata (MCA). The main finding of our simulations is formation of a boundary layer where intensive plastic deformation and mixing processes occur. The boundary layer is well localized and does not spread to deeper layers. We investigated how the thickness of the boundary layer and the friction force stemming from the processes in this layer do depend on parameters of material and loading. To this end, all the parameters involved in the numerical model have been varied and the average friction coefficient as well as thickness of the layer determined for each set of parameter. We found that at velocities much smaller than velocity of sound and normal pressures much smaller than the yield stress, the thickness of the quasi-fluid layer is proportional to effective viscosity of the medium and the friction coefficient does depend only on two dimensionless parameters: κ1=ρv2E/σ02 and κ2=PE/σ02.

A theory of the transition from static to kinetic friction in boundary lubrication layers

Abstract The behavior of a thin lubrication layer is described in a model combining the Landau theory of phase transformations and the Frenkel–Kontorova model. The kinetic equation for the shear modulus is obtained and solved together with the equation of overdamped motion of the layer. The maximum static and the minimum kinetic friction stresses as well as the dependence of kinetic friction stress on sliding velocity are calculated analytically. The state of the layer during sliding is determined by a dimensionless parameter κ. At small values of κ shearing of the layer causes its melting. For large values of κ no shear melting occurs: the stable state is that of solid-state sliding. The transition from the static to the kinetic friction occurs in an interval of extremely small velocities defined as a ratio of the lattice parameter to the relaxation time of the shear modulus.

Partial-slip frictional response of rough surfaces

If two elastic bodies with rough surfaces are first pressed against each other and then loaded tangentially, sliding will occur at the boundary of the contact area while the inner parts may still stick. With increasing tangential force, the sliding parts will expand while the sticking parts shrink and finally vanish. In this paper, we study the fractions of the contact area, tangential force and tangential stiffness, associated with the sticking portion of the contact area, as a function of the total applied tangential force up to the onset of full sliding. For the numerical analysis randomly rough, fractal surfaces are used, with the Hurst exponent H ranging from 0.1 to 0.9. Numerical simulations by boundary element method are compared with an analytical analysis in the framework of the Greenwood and Williamson (GW) model. In both cases, a universal linear dependency between the real contact area fraction in stick condition and the applied tangential force is found, regardless of the Hurst exponent of the rough surfaces. Regarding the dependence of the differential tangential stiffness on the tangential force, a linear relation is found in the GW case. For randomly rough surfaces, a nonlinear relation depending on H is derived.

Thermodynamics and kinetics of shear-induced melting of a thin layer of lubricant confined between solids

Using Landau’s phenomenological theory of phase transitions, the shear-induced melting of a thin layer of substance confined between two crystalline surfaces is considered. The kinetics of melting and solidification is considered for static and alternating loads. The possibility of two consecutive “melting” (solid-to-liquid) transitions is discussed. As a result of the first transition, modulation of the microscopic density becomes zero only in the direction of shear (partial melting) and as a result of the second, it also disappears in the normal direction (complete melting).