Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements

Sergei Rogosin, Gennady Mishuris, Anna Koroleva, Anastasiya Vinakurava

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
142 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)585-609
JournalMathematical Modelling and Analysis
Volume21
Issue number5
DOIs
Publication statusPublished - 20 Sept 2016

Keywords

  • articular cartilage layers
  • biphasic model
  • asymptotic representation
  • elliptic contact zone
  • tangential displacement

Fingerprint

Dive into the research topics of 'Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements'. Together they form a unique fingerprint.

Cite this