Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements. Issue 5 (2nd September 2016)

• Record Type: Journal Article
• Authors: Rogosin, Sergei; Mishuris, Gennady; Koroleva, Anna; Vinakurava, Anastasiya
• Is Part Of: Mathematical modelling and analysis. Volume 21:Issue 5(2016)
• Page Start: 585
• Page End: 609
• Publication Date: 2016-09-02
• Subjects: articular cartilage layers -- biphasic model -- asymptotic representation -- elliptic contact zone -- tangential displacement; 74G10 -- 74M15 -- 92C10; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2016.1196249
• Languages: English
• ISSNs: 1392-6292

Abstract

Abstract: A three-dimensional unilateral contact problem for articular cartilage layers attached to subchondral bones shaped as elliptic paraboloids is considered in the framework of the biphasic cartilage model. The main novelty of the study is in accounting not only for the normal (vertical), but also for tangential vertical (horizontal) displacements of the contacting surfaces. Exact general relationships have been established between the contact approach and some integral characteristics of the contact pressure, including the contact force. Asymptotic representations for the contact pressure integral characteristics are obtained in terms of the contact approach and some integral characteristics of the contact zone. The main result is represented by the first-order approximation problem. We supply the theoretical description of the asymptotic method by numerical analysis of the model. Our calculations demonstrate good convergence of the numerical scheme in determination of the parameters. In particular, it is shown that accounting for the tangential displacement is important in cases where the contact zone is non-circular.