Skip to main content

2015 | Buch

Contact Mechanics of Articular Cartilage Layers

Asymptotic Models

insite
SUCHEN

Über dieses Buch

This book presents a comprehensive and unifying approach to articular contact mechanics with an emphasis on frictionless contact interaction of thin cartilage layers. The first part of the book (Chapters 1–4) reviews the results of asymptotic analysis of the deformational behavior of thin elastic and viscoelastic layers. A comprehensive review of the literature is combined with the authors’ original contributions. The compressible and incompressible cases are treated separately with a focus on exact solutions for asymptotic models of frictionless contact for thin transversely isotropic layers bonded to rigid substrates shaped like elliptic paraboloids. The second part (Chapters 5, 6, and 7) deals with the non-axisymmetric contact of thin transversely isotropic biphasic layers and presents the asymptotic modelling methodology for tibio-femoral contact. The third part of the book consists of Chapter 8, which covers contact problems for thin bonded inhomogeneous transversely isotropic elastic layers and Chapter 9, which addresses various perturbational aspects in contact problems and introduces the sensitivity of articular contact mechanics.

This book is intended for advanced undergraduate and graduate students, researchers in the area of biomechanics, and engineers interested and involved in the analysis and design of thin-layer structures.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Deformation of a Thin Bonded Transversely Isotropic Elastic Layer
Abstract
In this chapter we study frictionless contact problems for a thin transversely isotropic elastic layer bonded to a rigid substrate and indented by a smooth absolutely rigid punch under the assumption that the layer thickness is relatively small compared to the characteristic size of the contact area. We apply a perturbation technique to obtain asymptotic solutions of different degrees of accuracy and formulate simple mathematical models (called asymptotic models) to describe the deformational behavior of a bonded compressible elastic layer in the thin-layer approximation. In particular, the effects of unilateral contact interaction (with a priori unknown contact area) and the tangential displacements at the contact interface (taken into account in formulating the contact condition) are considered. It is shown that the case of an incompressible layer requires special consideration.
Ivan Argatov, Gennady Mishuris
Chapter 2. Asymptotic Analysis of the Contact Problem for Two Bonded Elastic Layers
Abstract
The first part of the chapter deals with the distributional asymptotic analysis of the contact problem of frictionless unilateral interaction of two bonded elastic layers. The case of incompressible layer materials is thoroughly treated in the second part of the chapter, beginning in Sect. 2.4.
Ivan Argatov, Gennady Mishuris
Chapter 3. Unilateral Frictionless Contact of Thin Bonded Incompressible Elastic Layers
Abstract
This chapter is devoted to solving contact problems for thin bonded incompressible transversely isotropic elastic layers in the thin-layer approximation, based on the leading-order asymptotic model developed in Chap. 2.
Ivan Argatov, Gennady Mishuris
Chapter 4. Frictionless Contact of Thin Viscoelastic Layers
Abstract
The chapter begins with an introduction to linear viscoelastic theory, and then proceeds to a generalization of the elastic leading-order asymptotic models for the viscoelastic case, based on the correspondence principle. In Sect. 4.2, we consider the main features of the analytical technique for solving unilateral contact problems for a viscoelastic foundation. The axisymmetric contact problem for a thin bonded incompressible viscoelastic layer is analyzed in Sect. 4.3 and in the refined formulation accounting for tangential displacements in Sect. 4.4. Finally, in Sect. 4.5 we solve the problem of frictionless contact for thin incompressible viscoelastic layers bonded to rigid substrates shaped like elliptic paraboloids.
Ivan Argatov, Gennady Mishuris
Chapter 5. Linear Transversely Isotropic Biphasic Model for Articular Cartilage Layer
Abstract
In Sect. 5.1, we develop a linear biphasic theory for the case of a transversely isotropic elastic solid matrix with transverse isotropy of permeability. In Sects. 5.2 and 5.3, we consider the linear biphasic models of confined and unconfined compression, respectively, for the biphasic stress relaxation and the biphasic creep tests. Finally, in Sect. 5.4 we outline the biphasic poroviscoelastic model, which accounts for the inherent viscoelasticity of the solid matrix.
Ivan Argatov, Gennady Mishuris
Chapter 6. Contact of Thin Biphasic Layers
Abstract
In Sect. 6.1, a three-dimensional deformation problem for an articular cartilage layer is studied in the framework of the linear biphasic model. The articular cartilage bonded to subchondral bone is modeled as a transversely isotropic biphasic material consisting of a solid phase and a fluid phase. In Sect. 6.2, the same problem is reconsidered with the effect of inherent viscoelasticity of the solid matrix taken into account. The frictionless unilateral contact problem for the articular cartilage layers is considered in Sect. 6.3. It is assumed that the subchondral bones are rigid and shaped like elliptic paraboloids. The obtained short-time leading-order asymptotic solution is valid for monotonically increasing loading conditions.
Ivan Argatov, Gennady Mishuris
Chapter 7. Articular Contact Mechanics
Abstract
In this chapter, an asymptotic modeling methodology for tibio-femoral contact is developed, based on the asymptotic models of frictionless unilateral contact interaction between thin cartilage layers. In Sect. 7.1, the normal contact forces, which are needed for multibody dynamics simulations, are determined analytically based on the exact solution for elliptical contact between thin cartilage layers generally modeled as viscoelastic incompressible layers. In Sect. 7.2, the equivalent Hunt–Crossley model for articular contact is developed in the framework of the short-time contact model for thin bonded biphasic layers.
Ivan Argatov, Gennady Mishuris
Chapter 8. Contact of Thin Inhomogeneous Transversely Isotropic Elastic Layers
Abstract
In this chapter we consider contact problems for thin bonded inhomogeneous transversely isotropic elastic layers. In particular, in Sects. 8.1 and 8.2, the deformation problems are studied for the cases of elastic layers with the out-of-plane and thickness-variable inhomogeneous properties, respectively. In Sect. 8.3, the axisymmetric frictionless contact problems for thin incompressible inhomogeneous elastic layers are studied in detail in the framework of the leading-order asymptotic model. Finally, the deformation problem for a transversely isotropic elastic layer bonded to a rigid substrate, and coated with a very thin elastic layer made of another transversely isotropic material is analyzed in Sect. 8.4.
Ivan Argatov, Gennady Mishuris
Chapter 9. Sensitivity Analysis of Articular Contact Mechanics
Abstract
Asymptotic models of articular contact developed in the previous chapters assume, in particular, that the cartilage layers are of uniform thickness and are bonded to rigid substrates shaped like elliptic paraboloids. In this final chapter, treating the term “sensitivity” in a broad sense, we study the effects of deviation of the substrate’s shape from the elliptic (Sect. 9.1) and of nonuniform thicknesses of the contacting incompressible layers (Sect. 9.2). It is shown that these effects in multibody dynamics simulations can be minimized if the geometric parameters in question (in particular, the layer thicknesses) are determined in a specific way to minimize the corresponding error in the force-displacement relationship.
Ivan Argatov, Gennady Mishuris
Backmatter
Metadaten
Titel
Contact Mechanics of Articular Cartilage Layers
verfasst von
Ivan Argatov
Gennady Mishuris
Copyright-Jahr
2015
Electronic ISBN
978-3-319-20083-5
Print ISBN
978-3-319-20082-8
DOI
https://doi.org/10.1007/978-3-319-20083-5

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.