Contact Mechanics

Contact mechanics is a fundamental field of tribology and generally refers to the interaction of solid surfaces. This interaction or contact can occur on many different scales, ranging from nanoscale asperities up to tires on roads and even contact between tectonic plates. This chapter reviews the basic technical information available in predicting the contact area, pressure, stresses, and forces that occur when surfaces interact. The chapter considers different geometries such as spheres and wavy surfaces and also outlines how to consider elastic and plastic deformation. The phenomena of creep and adhesion that are important for many tribological applications, and especially biological contacts, are also discussed. Finally, the chapter concludes by covering methods used to model the complicated situation of contact between rough surfaces that contain many different geometrical features.

This paper introduces a new computer program called WEAR. It contains a new and more accurate method for calculating wheel–rail contact stresses to predict degradation due to wear, deformation and fatigue. WEAR accounts for conformal contact by using influence numbers that are based on quasi-quarter spaces instead of the traditional half-spaces and considers the varying geometrical spin due to the varying contact angle through a contact patch. This new contact method is applied to two cases: wheel–rail contact in a turnout and conformal contact in a curve with a heavily worn wheel profile. In both cases, many of the assumptions commonly made in excising solution methods for wheel–rail contact problems, such as a small contact patch and a constant spin creepage, may be violated. The case of conformal contact demonstrates the effect of the influence numbers and the varying spin creepage on the resulting stresses and creep forces and provides a comparison of this new method with the well-established contact method CONTACT. For the turnout case, the first task is to obtain realistic input for all timesteps of a vehicle coasting through a turnout (i.e., diverging route) in a simulation. This step is necessary because the contact forces, which cause wear, deformation and fatigue of the wheels and rails, and the dynamics of the vehicle-turnout interaction strongly influence each other. WEAR converged for all timesteps, including many cases with multiple-point contacts at the switch blade and with extremely high creepages. This robustness demonstrates suitability of the new method for online contact force evaluation in vehicle dynamics simulations.

This paper presents a study of the load-deformation behavior of geocell-stabilized subballast subjected to cyclic loading using a novel track process simulation apparatus. The tests were conducted at frequencies varying from 10 to 30 Hz. This frequency range is generally representative of Australian standard gauge trains operating up to 160 km=h. The discrete-element method (DEM) was also used to model geocell-reinforced subballast under plane strain conditions. The geocell was modeled by connecting a group of small circular balls together to form the desired geometry and aperture using contact and parallel bonds. Tensile and bending tests were carried out to calibrate the model parameters adopted for simulating the geocell. To model irregularly shaped particles of subballast, clusters of bonded circular balls were used. The simulated load-deformation curves of the geocell-reinforced subballast assembly at varying cyclic load cycles were in good agreement with the experimental observations. The results indicated that the geocell decreased the vertical and lateral deformation of subballast assemblies at any given frequency. Furthermore, the DEM can also provide insight into the distribution of contact force chains, and average contact normal and shear force distributions, which cannot be determined experimentally.

Durbi Takusheyi is a burial site composed of at least eight mounds located between the modern towns of Katsina and Daura in northern Nigeria. Parts of the mounds were first excavated in 1907 by Herbert Richmond Palmer in cooperation with the Emir of Katsina and later again in 1992 in the course of a German research project under the lead of Dierk Lange, Bayreuth. After the 1992 excavation, the retained blocks were stored in the Jos Museum, Nigeria, for further analyses. In 2007 the Römisch-Germanisches Zentralmuseum (RGZM) and the National Commission for Museums and Monuments in Nigeria (NCMM) started a project with the objective of completely restoring and analyzing the excavated artefacts.While the remains of the first excavation appear to be lost with only minimal information preserved, the three mounds excavated in 1992 each contained a single interment in the centre of the mound, all three with various burial goods produced from inorganic (metal, glass, stone, cowries) and organic material (cloth, wood, hides). Many artefacts are of regional provenance but some were also imported from distant regions of the Islamic world. Following the currently available radiocarbon measurements, one group of the burials would date to the earlier fourteenth century AD, and judging from typology and art history another burial dates to the later fifteenth/early sixteenth centuries. The site thus covers a crucial phase in history during which the Hausa city states emerged, indicating shifting contacts to the Mediterranean and to the Middle East.Durbi Takusheyi est un site funéraire constitué d'au moins huit buttes, situé entre les villes moderns de Daura et Katsina an nord du Nigeria. Une partie des buttes furent fouillées en 1907 par Herbert Richmond Palmer, en collaboration avec l’émir du Katsina, puis en 1992 au cours d'un projet de recherche allemand dirigé par Dier Lange, Bayreuth. À la suite des fouilles de 1992, des blocs de matériel furent déposés dans les remises du musée de Jos (Nigeria) dans l'attente d'analyses futures. En 2007 le Römisch-Germanisches Zentralmuseum (RGZM) et la National Commission for Museums and Monuments du Nigeria (NCMM) débutèrent un projet dont l'objectif est d'analyser et de restaurer totalement les artéfacts issus des fouilles.Les objets issus des fouilles de 1907 semblent avoir disparu, et seul le minimum d'informations subsiste. Pour ce qui est des fouilles de 1992, cependant, on sait que chacune des trois buttes fouillées contenait une sépulture en son centre, avec un mobilier divers constitué de matériaux inorganiques (métal, verre, pierre, cauris) et organiques (textiles, bois, peaux). Beaucoup des objets sont de provenance locale, mais d'autres furent importés de régions distantes du monde islamique. À la base des datations radiocarbon dont on dispose, il semble que l'un des groupes de sépultures date du début du XIVème siècle ap. J-C, et les données typologiques et d'histoire de l'art indiquent qu'une autre inhumation date de la fin du XVème/début XVIème. Le site date ainsi d'une période cruciale de l'histoire, durant laquelle émergèrent les cites-état hausa, indiquant des contacts changeants avec la Méditerranée et le Moyen-Orient.