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Contact mechanics is the study of the deformation of solids that touch each other at one or more points. This can be divided into compressive and adhesive forces in the direction perpendicular to the interface, and frictional forces in the tangential direction. Frictional contact mechanics is the study of the deformation of bodies in the presence of frictional effects, whereas ''frictionless contact mechanics'' assumes the absence of such effects. Frictional contact mechanics is concerned with a large range of different scales. * At the macroscopic scale, it is applied for the investigation of the motion of contacting bodies (see Contact dynamics). For instance the bouncing of a rubber ball on a surface depends on the frictional interaction at the contact interface. Here the total force versus indentation and lateral displacement are of main concern. * At the intermediate scale, one is interested in the local stresses, strains and deformations of the contacting bodies in and near the contact area. For instance to derive or validate contact models at the macroscopic scale, or to investigate wear and damage of the contacting bodies’ surfaces. Application areas of this scale are tire-pavement interaction, railway wheel-rail interaction, roller bearing analysis, etc. * Finally, at the microscopic and nano-scales, contact mechanics is used to increase our understanding of tribological systems, e.g. investigate the origin of friction, and for the engineering of advanced devices like atomic force microscopes and MEMS devices. This page is mainly concerned with the second scale: getting basic insight in the stresses and deformations in and near the contact patch, without paying too much attention to the detailed mechanisms by which they come about. == History == Several famous scientists and engineers contributed to our understanding of friction.〔(【引用サイトリンク】 Introduction to Tribology – Friction )〕 They include Leonardo da Vinci, Guillaume Amontons, John Theophilus Desaguliers, Leonhard Euler, and Charles-Augustin de Coulomb. Later, Nikolai Pavlovich Petrov, Osborne Reynolds and Richard Stribeck supplemented this understanding with theories of lubrication. Deformation of solid materials was investigated in the 17th and 18th centuries by Robert Hooke, Joseph Louis Lagrange, and in the 19th and 20th centuries by d’Alembert and Timoshenko. With respect to contact mechanics the classical contribution by Heinrich Hertz stands out. Further the fundamental solutions by Boussinesq and Cerruti are of primary importance for the investigation of frictional contact problems in the (linearly) elastic regime. Classical results for a true frictional contact problem concern the papers by F.W. Carter (1926) and H. Fromm (1927). They independently presented the creep versus creep force relation for a cylinder on a plane or for two cylinders in steady rolling contact using Coulomb’s dry friction law (see below). These are applied to railway locomotive traction, and for understanding the hunting oscillation of railway vehicles. With respect to sliding, the classical solutions are due to C. Cattaneo (1938) and R.D. Mindlin (1949), who considered the tangential shifting of a sphere on a plane (see below).〔 In the 1950s interest in the rolling contact of railway wheels grew. In 1958 K.L. Johnson presented an approximate approach for the 3D frictional problem with Hertzian geometry, with either lateral or spin creepage. Among others he found that spin creepage, which is symmetric about the center of the contact patch, leads to a net lateral force in rolling conditions. This is due to the fore-aft differences in the distribution of tractions in the contact patch. In 1967 Joost Kalker published his milestone PhD thesis on the linear theory for rolling contact. This theory is exact for the situation of an infinite friction coefficient in which case the slip area vanishes, and is approximative for non-vanishing creepages. It does assume Coulomb’s friction law, which more or less requires (scrupulously) clean surfaces. This theory is for massive bodies such as the railway wheel-rail contact. With respect to road-tire interaction, an important contribution concerns the so-called magic tire formula by Hans Pacejka. In the 1970s many numerical models were devised. Particularly variational approaches, such as those relying on Duvaut and Lion’s existence and uniqueness theories. Over time, these grew into finite element approaches for contact problems with general material models and geometries, and into half-space based approaches for so-called smooth-edged contact problems for linearly elastic materials. Models of the first category were presented by Laursen〔Laursen, T.A., 2002, ''Computational Contact and Impact Mechanics, Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis'', Springer, Berlin〕 and by Wriggers.〔Wriggers, P., 2006, ''Computational Contact Mechanics, 2nd ed.'', Springer, Heidelberg〕 An example of the latter category is Kalker’s CONTACT model. A drawback of the well-founded variational approaches is their large computation times. Therefore many different approximate approaches were devised as well. Several well-known approximate theories for the rolling contact problem are Kalker’s FASTSIM approach, the Shen-Hedrick-Elkins formula, and Polach’s approach. More information on the history of the wheel/rail contact problem is provided in Knothe's paper.〔 Further Johnson collected in his book a tremendous amount of information on contact mechanics and related subjects.〔 With respect to rolling contact mechanics an overview of various theories is presented by Kalker as well. Finally the proceedings of a CISM course are of interest, which provide an introduction to more advanced aspects of rolling contact theory. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Frictional contact mechanics」の詳細全文を読む スポンサード リンク
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