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The Resource Contact Mechanics of Articular Cartilage Layers : Asymptotic Models

Contact Mechanics of Articular Cartilage Layers : Asymptotic Models

Label
Contact Mechanics of Articular Cartilage Layers : Asymptotic Models
Title
Contact Mechanics of Articular Cartilage Layers
Title remainder
Asymptotic Models
Creator
Contributor
Subject
Language
eng
Summary
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
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Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Advanced Structured Materials Ser.
Series volume
v.50
Contact Mechanics of Articular Cartilage Layers : Asymptotic Models
Label
Contact Mechanics of Articular Cartilage Layers : Asymptotic Models
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=2120608
Publication
Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Acknowledgments -- Contents -- 1 Deformation of a Thin Bonded Transversely Isotropic Elastic Layer -- 1.1 Deformation Problem Formulation -- 1.2 Perturbation Analysis of the Deformation Problem -- 1.3 Contact Problem Formulation for a Thin Elastic Layer -- 1.4 Asymptotic Solution of the Contact Problem for a Thin Bonded Compressible Elastic Layer -- 1.5 Asymptotic Models for the Beformation Response of a Thin Bonded Compressible Elastic Layer -- 1.5.1 Zeroth-Order Asymptotic Model for the Contact Problem -- 1.5.2 Asymptotic Model for the Pasternak Foundation -- 1.5.3 Refined Contact Model with Allowance for Tangential Displacements on the Contact Interface -- References -- 2 Asymptotic Analysis of the Contact Problem for Two Bonded Elastic Layers -- 2.1 Contact Problem Formulation -- 2.1.1 Geometry of Surfaces in Contact -- 2.1.2 Unilateral Contact Conditions -- 2.1.3 Governing Integral Equation -- 2.2 Distributional Asymptotic Analysis -- 2.2.1 Moment Asymptotic Expansion for the Integral Operator of the Frictionless Contact Problem for a Thin Elastic Layer -- 2.2.2 Asymptotic Solution of the Contact Problem for Slightly Curved Thin Compressible Elastic Layers -- 2.2.3 Comparison of the Results Obtained by the Perturbation and Distributional Asymptotic Methods -- 2.3 Boundary-Layer Problem in the Compressible Case -- 2.3.1 Variation of the Contact Area -- 2.3.2 Boundary-Layer Integral Equation -- 2.3.3 Aleksandrov's Approximation -- 2.3.4 Boundary-Layer in the Compressible Case -- 2.4 Incompressible Transversely Isotropic Elastic Material -- 2.4.1 Stress-Strain Relations for Incompressible Material -- 2.4.2 Isotropically Compressible Transversely Isotropic Materials -- 2.5 Deformation of a Thin Incompressible Transversely Isotropic Elastic {u0083}
  • 2.5.1 Perturbation Analysis of the Deformation Problem for a Thin Incompressible Elastic Layer -- 2.5.2 Local Indentation of a Thin Weakly Compressible Elastic Layer -- 2.6 Boundary-Layer Problem in the Incompressible Case -- 2.6.1 Transformation of the Governing Integral Equation -- 2.6.2 Boundary-Layer Integral Equation -- 2.6.3 Special Solutions of the Boundary-Layer Integral Equation -- 2.6.4 Solution of the Boundary-Layer Integral Equation with a Polynomial Right-Hand Side -- 2.6.5 Approximate Solution of the Boundary-Layer Integral Equation -- 2.7 Leading-Order Asymptotic Solution of the Contact Problem for Incompressible Layers -- 2.7.1 Governing Differential Equation -- 2.7.2 Boundary Condition in the Case of Fixed Contact Area -- 2.7.3 Boundary Conditions in the Case of Unilateral Contact -- References -- 3 Unilateral Frictionless Contact of Thin Bonded Incompressible Elastic Layers -- 3.1 Asymptotic Model for the Frictionless Contact of Thin Bonded Incompressible Layers -- 3.1.1 Leading-Order Asymptotic Model for the Unilateral Contact -- 3.1.2 Elliptical Contact of Thin Bonded Incompressible Elastic Layers -- 3.1.3 Similarity Analysis of the Contact Problem for Thin Bonded Incompressible Elastic Layers -- 3.2 Axisymmetric Refined Contact Problem for Thin Bonded Incompressible Elastic Layers, with Allowance for Tangential Displacements on the Contact Interface -- 3.2.1 Refined Formulation of the Axisymmetric Contact Problem -- 3.2.2 Equation for the Contact Approach -- 3.2.3 Equation for the Contact Radius -- 3.2.4 Contact Pressure -- 3.2.5 Approximate Equation for the Radius of the Contact Area -- 3.2.6 Approximate Solution -- 3.3 Refined Contact Model for a Thin Bonded Incompressible Elastic Layer with the Effect of Tangential Displacements -- 3.3.1 Refined Formulation of the Contact Problem
  • 3.3.2 Approximate Solution for the Contact Pressure -- 3.3.3 Asymptotic Solution of the Resulting Algebraic Problem -- 3.3.4 Approximation for the Contact Area -- 3.3.5 Equation for the Contact Force -- 3.3.6 Variation of the Contact Area -- 3.3.7 Comparison with the Solution of the Axisymmetric Problem -- References -- 4 Frictionless Contact of Thin Viscoelastic Layers -- 4.1 Deformation of a Thin Viscoelastic Layer -- 4.1.1 Viscoelastic Constitutive Laws -- 4.1.2 Correspondence Principle for a Viscoelastic Layer -- 4.1.3 Deformation of a Thin Compressible Transversely Isotropic Viscoelastic Layer Bonded to a Rigid Base -- 4.1.4 Deformation of a Thin Bonded Incompressible Transversely Isotropic Viscoelastic Layer -- 4.2 Axisymmetric Contact of Thin Compressible Viscoelastic Layers -- 4.2.1 Contact Problem Formulation -- 4.2.2 Axial Aggregate Relaxation and Creep Functions -- 4.2.3 Instantaneous Contact -- 4.2.4 Monotonically Increasing Contact Area -- 4.2.5 Monotonically Increasing Contact Area: Contact Pressure -- 4.2.6 Case of Stepwise Loading -- 4.2.7 Monotonically Decreasing Contact Area -- 4.2.8 Case of Stepwise Displacement-Controlled Loading -- 4.3 Axisymmetric Contact of Thin Incompressible Viscoelastic Layers: Monotonically Increasing Contact Area -- 4.3.1 Formulation of the Contact Problem -- 4.3.2 Equation for the Contact Approach -- 4.3.3 Equation for the Radius of the Contact Area -- 4.3.4 Example: General Paraboloid of Revolution -- 4.3.5 Contact Pressure Distribution -- 4.3.6 Example: Paraboloid of Revolution -- 4.4 Axisymmetric Refined Contact Problem for a Thin Bonded Incompressible Viscoelastic Layer with Allowance for Tangential Displacements on the Contact Surface -- 4.4.1 Refined Formulation of the Contact Problem -- 4.4.2 Equation for the Punch Displacement -- 4.4.3 Equation for the Radius of Contact Area
  • 4.4.4 Contact Pressure -- 4.5 Elliptical Contact of Thin Bonded Incompressible Viscoelastic Layers: Monotonically Increasing Contact Area -- 4.5.1 Formulation of the Contact Problem -- 4.5.2 General Solution for the Case of Elliptical Contact -- 4.5.3 Case of Stepwise Loading -- 4.5.4 Axisymmetric Contact Problem for Incompressible Coatings: Case of Stepwise Loading -- 4.5.5 Case of Incompressible Layers Following the Maxwell Model -- 4.5.6 Force-Displacement Relationship -- References -- 5 Linear Transversely Isotropic Biphasic Model for Articular Cartilage Layer -- 5.1 Linear Biphasic Model -- 5.1.1 Linear Biphasic Theory -- 5.1.2 Boundary and Initial Conditions -- 5.1.3 Equivalent Elastic Material Properties of a Transversely Isotropic Biphasic Material for the Instantaneous Response -- 5.1.4 Axisymmetric Biphasic Model -- 5.2 Confined Compression of a Biphasic Material -- 5.2.1 Confined Compression Problem -- 5.2.2 Governing Equation of the Confined Compression Model -- 5.2.3 Biphasic Stress Relaxation in Confined Compression -- 5.2.4 Biphasic Creep in Confined Compression -- 5.2.5 Dynamic Behavior of a Biphasic Material Under Cyclic Compressive Loading in Confined Compression -- 5.3 Unconfined Compression of a Biphasic Material -- 5.3.1 Unconfined Compression Problem -- 5.3.2 Solution of the Unconfined Compression Problem -- 5.3.3 Unconfined Compression Model -- 5.3.4 Biphasic Stress Relaxation in Unconfined Compression -- 5.3.5 Biphasic Creep in Unconfined Compression -- 5.3.6 Cyclic Compressive Loading in Unconfined Compression -- 5.3.7 Displacement-Controlled Unconfined Compression Test -- 5.3.8 Force-Controlled Unconfined Compression Test -- 5.4 Biphasic Poroviscoelastic (BPVE) Model -- 5.4.1 Linear Biphasic Poroviscoelastic Theory -- 5.4.2 Confined Compression of a Biphasic Poroviscoelastic Material
  • 5.4.3 Unconfined Compression of a BPVE Material -- 5.4.4 Torsion of a Biphasic Poroviscoelastic Material -- References -- 6 Contact of Thin Biphasic Layers -- 6.1 Deformation of a Thin Bonded Biphasic Layer -- 6.1.1 Deformation Problem Formulation -- 6.1.2 Perturbation Analysis of the Deformation Problem: Short-Time Asymptotic Solution -- 6.1.3 Solution of the Resulting Ordinary Boundary-Value Problem -- 6.1.4 Displacements of the Solid Matrix -- 6.1.5 Interstitial Fluid Pressure and Relative Fluid Flux -- 6.1.6 Stresses in the Solid and Fluid Phases -- 6.1.7 Long-Term (Equilibrium) Response of a Thin Bonded Biphasic Layer Under Constant Loading -- 6.2 Deformation of a Thin Transversely Isotropic Biphasic Poroelastic Layer Bonded to a Rigid Impermeable Substrate -- 6.2.1 Deformation Problem Formulation -- 6.2.2 Short-Time Asymptotic Analysis of the Deformation Problem -- 6.2.3 Local Indentation of a Thin BPVE Layer -- 6.2.4 Reduced Relaxation and Creep Function for the Fung Model -- 6.3 Contact of Thin Bonded Transversely Isotropic BPVE Layers -- 6.3.1 Contact Problem Formulation for BPVE Cartilage Layers -- 6.3.2 Exact Solution for Monotonic Loading -- References -- 7 Articular Contact Mechanics -- 7.1 Asymptotic Modeling Methodology for Tibio-Femoral Contact -- 7.1.1 Articular Contact in Multibody Dynamics -- 7.1.2 Articular Cartilage Structure and Models -- 7.1.3 Articular Surface Geometry -- 7.1.4 Contact Constitutive Relation. Elliptical Contact of Thin Incompressible Elastic Layers -- 7.1.5 Asymptotic Model for Elliptical Contact of Thin Incompressible Viscoelastic Layers -- 7.1.6 Approximation of the Articular Femur and Tibia Geometries by Elliptic Paraboloids -- 7.1.7 Determining the Effective Geometrical Characteristics from Experimental Surface Data -- 7.1.8 Generalization of the Contact Constitutive Relation
  • 7.1.9 Modified Incomplete Storage Shear Modulus and Loss Angle
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1 online resource (348 pages)
Form of item
online
Isbn
9783319200835
Media category
computer
Media MARC source
rdamedia
Media type code
c
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