| Summary: | In skeletal joints two layers of adjacent cartilage are often in relative motion. The individual cartilage
layers are often modelled as a poroviscoelastic material. To model the relative motion, noting Using the
separation of scales between the pore level and the macroscale, a homogenisation based on multiple scale
asymptotic analysis has been used in this study to derive a macroscale model for the relative translation of
two poroviscoelastic layers separated by a very thin layer of fluid. In particular the fluid layer thickness
is essentially zero at the macroscale so that the two poroviscoelastic layers are effectively in contact and
their interaction is captured in the derived model via a set of interfacial conditions, including a generalisation of the Beavers-Joseph condition at the interface between a viscous fluid and a porous medium.
This derivation is motivated by modelling the relative motion of articular cartilage within skeletal joints.
In the simplifying context of a uniform geometry, constant fixed charge density, a Newtonian interstitial
fluid and a viscoelastic scaffold, modelled via finite deformation theory, we present preliminary simulations that may be used to highlight predictions for how oscillatory relative movement of cartilage under
load influences the peak force the cartilage experiences and the extent of the associated deformations.
In addition to highlighting such cartilage mechanics, the systematic derivation of the macroscale models
will enable the study of how nanoscale cartilage physics, such as the swelling pressure induced by fixed
charges, manifests in cartilage mechanics at much higher lengthscales.
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