By Ivan Argatov, Gennady Mishuris
This booklet offers a accomplished and unifying method of articular touch mechanics with an emphasis on frictionless touch interplay of skinny cartilage layers. the 1st a part of the ebook (Chapters 1–4) stories the result of asymptotic research of the deformational habit of skinny elastic and viscoelastic layers. A finished evaluation of the literature is mixed with the authors’ unique contributions. The compressible and incompressible instances are taken care of individually with a spotlight on precise suggestions for asymptotic types of frictionless touch for skinny transversely isotropic layers bonded to inflexible substrates formed like elliptic paraboloids. the second one half (Chapters five, 6, and seven) offers with the non-axisymmetric touch of skinny transversely isotropic biphasic layers and provides the asymptotic modelling technique for tibio-femoral touch. The 3rd a part of the publication comprises bankruptcy eight, which covers touch difficulties for skinny bonded inhomogeneous transversely isotropic elastic layers and bankruptcy nine, which addresses numerous perturbational elements in touch difficulties and introduces the sensitivity of articular touch mechanics.
This booklet is meant for complex undergraduate and graduate scholars, researchers within the quarter of biomechanics, and engineers and serious about the research and layout of thin-layer structures.
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Extra info for Contact Mechanics of Articular Cartilage Layers: Asymptotic Models
76) with unknown parameters p0 , a, and b. 76) into Eq. 75) gives y2 y2 h p0 1 − 12 − 22 A33 a b − (A44 − A13 )h 2 A33 A44 y12 y22 + R1 a 2 R2 b 2 = δ0 − y12 y2 − 2 . 77) . 78) where R = 2R1 R2 /(R1 + R2 ) is the harmonic mean of the curvature radii R1 and R2 . Note also that in writing Eq. 78), we have neglected the terms of order O((h/R)2 ). 5 Asymptotic Models for the Beformation Response … 17 In the case of isotropic material, (A44 − A13 )/A44 = (1 − 4ν)/(1 − 2ν), and, as can be seen from Eqs.
It is noteworthy that the phenomenological approach has a disadvantage in that the parameters k P and G P are difficult to determine . 46) yields the following response function: p(y) A13 (A44 − A13 ) A33 w0 (y) − hΔ y w0 (y). 69) Now, comparing Eqs. 69), we obtain the relations kP = A33 A13 (A44 − A13 ) , GP = h. 70) In the case of an isotropic material, we have kP = E(1 − ν) Eν(1 − 4ν)h , GP = . 71)2 produces a negative value for the parameter G P . 68) when the layer material is sufficiently compressible.
Rend. Mat. e Appl. 18, 95–139 (1959) 36. : Anisotropic Elasticity. Oxford University Press, Oxford (1996) 37. : Beams, Plates and Shells on Elastic Foundation [in Russian]. Fizmatgiz, Moscow (1960). English translation, Israel Program for Scientific Translations, Jerusalem (1966) 38. : Beams and plates on elastic foundations: a review. Prog. Struct. Eng. Mater. 7, 174–182 (2005) 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.
Contact Mechanics of Articular Cartilage Layers: Asymptotic Models by Ivan Argatov, Gennady Mishuris