By Ivan Argatov, Gennady Mishuris
This e-book offers a finished 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) studies the result of asymptotic research of the deformational habit of skinny elastic and viscoelastic layers. A entire overview of the literature is mixed with the authors’ unique contributions. The compressible and incompressible instances are handled individually with a spotlight on targeted suggestions for asymptotic versions 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) bargains with the non-axisymmetric touch of skinny transversely isotropic biphasic layers and provides the asymptotic modelling method for tibio-femoral touch. The 3rd a part of the publication contains bankruptcy eight, which covers touch difficulties for skinny bonded inhomogeneous transversely isotropic elastic layers and bankruptcy nine, which addresses a number of perturbational facets involved difficulties and introduces the sensitivity of articular touch mechanics.
This booklet is meant for complicated undergraduate and graduate scholars, researchers within the quarter of biomechanics, and engineers and inquisitive about the research and layout of thin-layer structures.
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Extra resources for Contact Mechanics of Articular Cartilage Layers: Asymptotic Models
Following , we consider anisotropic materials which under a uniform hydrostatic pressure exhibit strictly isotropic volumetric response. In this case, the bulk modulus, K , of such an isotropically compressible material is independent of the stress state and represents its intrinsic property. For an isotropically compressible transversely isotropic material, the number of independent material constants is equal to 4, while E, E , G , and K can be taken, in this instance. 4 Incompressible Transversely Isotropic Elastic Material ν = 45 E E 1 1 1 , G= − , ν =1− + 2 6K 2 E 3K E E E E 4E − E − 3K .
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. 40), which can be rewritten as w0 (y) + ∇ y ϕ(y) · v0 (y) = δ0 − ϕ(y). 72) 16 1 Deformation of a Thin Bonded Transversely Isotropic Elastic Layer Here, w0 and v0 are the normal and tangential displacements of the surface points of the elastic layer on the contact interface. In the framework of the first-order asymptotic model, we have h p, A33 A44 − A13 2 v0 = h ∇ y p.
67), and analytically as the next higher approximation. 68) where k P and G P are the foundation constants. The Pasternak foundation can be constructed by connecting a layer of the Winkler spring elements to a surface layer of vertically incompressible elements which deform in transverse shear only . 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).
Contact Mechanics of Articular Cartilage Layers: Asymptotic Models by Ivan Argatov, Gennady Mishuris