Method of reduction of dimensionality in contact and friction mechanics: A linkage between micro and macro scales

• DOI: 10.1007/s40544-013-0005-3
• Publication Date: 2013-03-25T17:46:40Z
• Authors: Valentin L. Popov
• Keywords: Contact Mechanics; Indentation; Contact area; Macro

Abstract Computer simulations have been an integral part of the technical development process for a long time now. Industrial tribology is one last fields in which computer have, until now, played no significant role. This primarily due to fact that investigating tribological phenomena requires considering all spatial scales from macroscopic shape contact system down micro-scales. In present paper, we give overview previous work on so-called method reduction dimensionality (MRD), our opinion, gives key linking micro- and macro-scales simulations. MRD mechanics based mapping some classes three-dimensional problems onto one-dimensional contacts with elastic foundations. The equivalence systems those one-dimension valid relations indentation depth force cases area. For arbitrary bodies revolution, exact provides sort “pocket edition” mechanics, giving possibility deriving any result classical or without adhesion very simple way. A tangential problem creep can also be mapped exactly system. It shown applicable linear visco-elastic as well thermal effects contacts. was further validated randomly rough self-affine surfaces through comparison direct 3D means huge computational simulation friction between accounting complicated rheology adhesion. MRD, not only dimension space reduced three one, but resulting degrees freedom are independent (like normal modes theory oscillations). Because this independence, predestinated parallel calculation graphic cards, brings acceleration. opens completely new possibilities combining microscopic dynamics determining “law friction” intermediate step.