Asymptotic behaviour of thin poroelastic layers

Barry, Steven

doi:10.1093/imamat/66.2.175

Cited by 36 publications

(44 citation statements)

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“…2 P matching the analysis of Barry & Holmes (2001). We also note that in the limit K u → ∞, equation (2.7) matches expressions for isotropic media derived by Rice & Cleary (1976), while the expression for b, equation (2.8), can be rewritten in the form derived earlier by Loret et al (2001).…”

Section: An Effective Poroelastic Field Theorysupporting

confidence: 68%

“…(ii) We illustrate how the anisotropic nature of both bed permeability and elasticity due to the alignment of the fibres may be properly accounted in the theory. Our work builds on previous studies of anisotropic poroelasticity (Biot 1941(Biot , 1955Barry & Holmes 2001), but includes and clarifies the role of boundary conditions in controlling the elastic properties of the bed. (iii) Finally, we show that matching of shear and normal stress at the composite-free liquid interface and complete flowdeformation coupling are both accomplished naturally using a Darcy-type model (Darcy 1856) describing relative flow between the solid and fluid phases in the soft medium.…”

Section: Introductionmentioning

confidence: 84%

“…The correct boundary conditions at a porous interface have been a source of longstanding debate owing to the problem of matching of both normal and tangential stresses at the interface (see Beavers & Joseph 1967;Saffman 1971;Taylor 1971;Hou et al 1989;Barry & Holmes 2001;Jager & Mikeli 2009;Nield 2009). Previous models for the flow through porous media (Fredrickson & Pincus 1991;Feng & Weinbaum 2000;Du et al 2004) use the Brinkman equation and its variants that take the form…”

Section: Boundary Conditionsmentioning

confidence: 99%

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Elastohydrodynamics of wet bristles, carpets and brushes

Gopinath

Mahadevan

2011

Proc. R. Soc. A.

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Surfaces covered by bristles, hairs, polymers and other filamentous structures arise in a variety of natural settings in science such as the active lining of many biological organs, e.g. lungs, reproductive tracts, etc., and have increasingly begun to be used in technological applications. We derive an effective field theory for the elastohydrodynamics of ordered brushes and disordered carpets that are made of a large number of elastic filaments grafted on to a substrate and interspersed in a fluid. Our formulation for the elastohydrodynamic response of these materials leads naturally to a set of constitutive equations coupling bed deformation to fluid flow, accounts for the anisotropic properties of the medium, and generalizes the theory of poroelasticity to these systems. We use the effective medium equations to study three canonical problems-the normal settling of a rigid sphere onto a carpet, the squeeze flow in a carpet and the tangential shearing motion of a rigid sphere over the carpet, all problems of relevance in mechanosensation in biology with implications for biomimetic devices.

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Section: An Effective Poroelastic Field Theorysupporting

confidence: 68%

Section: Introductionmentioning

confidence: 84%

Section: Boundary Conditionsmentioning

confidence: 99%

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Elastohydrodynamics of wet bristles, carpets and brushes

Gopinath

Mahadevan

2011

Proc. R. Soc. A.

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“…where F (1) and F (2) are the shear forces and M (1) and M (2) are the bending moments along the principal axes, F (3) is the tensile force and M (3) is the twisting moment.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of poroelastic filaments

Mahadevan

2004

Proc. R. Soc. Lond. A

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We investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition to the usual terms for the bending of an elastic rod, we find a term that arises from fluid-solid interaction. Using the poroelastica equation as a starting point, we consider the load controlled and displacement controlled planar buckling of a slender rod, as well as the closely related instabilities of a rod subject to twisting moments and compression when embedded in an elastic medium. This work has applications to the active and passive mechanics of thin filaments and sheets made from gels, plant organs such as stems, roots and leaves, sponges, cartilage layers and bones.

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“…Collins [9] considered Biot's theory to model poroelastic matrix for cartilage, which is assumed to satisfy the generalized form of Darcy's law for unsteady flow in an elastic porous medium. Later, modified and corrected forms of the constitutive equations are given in [10][11][12]. Most of the studies on synovial joint mechanics and lubrication have used elastic single-phase models of cartilage and a Newtonian single-phase model for synovial fluid.…”

Section: Introductionmentioning

confidence: 99%

Analysis of modified Reynolds equation using the wavelet‐multigrid scheme

Bujurke

Salimath

Kudenatti

et al. 2006

Numerical Methods Partial

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The combined study of effects of surface roughness and poroelasticity on the squeeze film behavior of bearings in general and that of synovial joints in particular are presented. The modified form of Reynolds equation, which incorporates the randomized roughness structure as well as elastic nature of articular cartilage, is derived. Christensen stochastic theory describing roughness structure of cartilage surfaces is used by assuming the roughness asperity heights to be small compared to the film thickness. A recently developed wavelet-multigrid method is used for the solution of Reynolds equation. The method has the greatest advantage of minimizing the errors using wavelet transforms in obtaining accurate solution, as grid size tends to zero. Based on the results obtained, the influence of roughness and elasticity on bearing characteristics are discussed in some detail.

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Asymptotic behaviour of thin poroelastic layers

Cited by 36 publications

References 0 publications

Elastohydrodynamics of wet bristles, carpets and brushes

Elastohydrodynamics of wet bristles, carpets and brushes

Dynamics of poroelastic filaments

Analysis of modified Reynolds equation using the wavelet‐multigrid scheme

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