Poroelastic materials reinforced by statistically oriented fibres--numerical implementation and application to articular cartilage

Tomic, Aleksandar; Grillo, Alfio; Federico, Salvatore

doi:10.1093/imamat/hxu039

Cited by 63 publications

(96 citation statements)

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“…We base the forthcoming description of the kinematics of biphasic mixtures on the theory developed in [87,88], and recently summarised in [94]. We denote by M s and M f the two smooth three-dimensional material manifolds associated with the matrix and the fluid, respectively.…”

Section: Kinematics Of Biphasic Mixturesmentioning

confidence: 99%

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A poroplastic model of structural reorganisation in porous media of biomechanical interest

Grillo

Prohl

Wittum

2015

Continuum Mech. Thermodyn.

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We present a poroplastic model of structural reorganisation in a binary mixture comprising a solid and a fluid phase. The solid phase is the macroscopic representation of a deformable porous medium, which exemplifies the matrix of a biological system (consisting e.g. of cells, extracellular matrix, collagen fibres). The fluid occupies the interstices of the porous medium and is allowed to move throughout it. The system reorganises its internal structure in response to mechanical stimuli. Such structural reorganisation, referred to as remodelling, is described in terms of "plastic" distortions, whose evolution is assumed to obey a phenomenological flow rule driven by stress. We study the influence of remodelling on the mechanical and hydraulic behaviour of the system, showing how the plastic distortions modulate the flow pattern of the fluid, and the distributions of pressure and stress inside it. To accomplish this task, we solve a highly nonlinear set of model equations by elaborating a previously developed numerical procedure, which is implemented in a non-commercial finite element solver.

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Section: Kinematics Of Biphasic Mixturesmentioning

confidence: 99%

“…[25,81,91]). Here, they have been adapted from [15,56] to the case of an incompressible, single-constituent fluid phase, as previously done in [34,35,45,94]. By substituting (8a) and (8b) into (6a) and (6b), the momentum balance laws for the mixture as a whole and for the fluid phase become [56] div…”

Section: Constitutive Framework and Remodelling Lawmentioning

confidence: 99%

A poroplastic model of structural reorganisation in porous media of biomechanical interest

Grillo

Prohl

Wittum

2015

Continuum Mech. Thermodyn.

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“…The material equations (54) have been shown for the case of Darcy's law [1,3,11,[15][16][17]23,25], as well as for the analogous case of the polarisation of a dielectric [5,6,9,19,26,27], in the traditional manner, without the use of differential forms. In some cases, the flux density pseudo-vector w may be given as the product of a pseudo-scalar density ρ times a proper vector field v, i.e.…”

Section: Application To First-order Transport Lawsmentioning

confidence: 99%

Material description of fluxes in terms of differential forms

Federico

Grillo

Segev

2015

Continuum Mech. Thermodyn.

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The flux of a certain extensive physical quantity across a surface is often represented by the integral over the surface of the component of a pseudo-vector normal to the surface. A pseudo-vector is in fact a possible representation of a second-order differential form, i.e. a skew-symmetric second-order covariant tensor, which follows the regular transformation laws of tensors. However, because of the skew-symmetry of differential forms, the associated pseudo-vector follows a transformation law that is different from that of proper vectors, and is named after the Italian mathematical physicist Gabrio Piola (1794-1850). In this work, we employ the methods of Differential Geometry and the representation in terms of differential forms to demonstrate how the flux of an extensive quantity transforms from the spatial to the material point of view. After an introduction to the theory of differential forms, their transformation laws, and their role in integration theory, we apply them to the case of first-order transport laws such as Darcy's law and Ohm's law.

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“…To this end, the free energy (1) is modified to account for the elastic behaviour of the solid part of the mixture with reference volume fraction φ sR . Using a term U (J) that enforces incompressibility at the compaction limit J → φ sR , as proposed in [5], and describing the fluid flow by Darcy's law [6], the free energy of the mixture and the fluid flux are given, respectively, by cf. [5,6] …”

Section: Bi-phasic Formulationmentioning

confidence: 99%

“…The hydraulic conductivity tensor is assumed isotropic, so that in the reference configuration H = Jk 0 (J)C −1 [6][7][8], where C = F T F. The model was implemented in COMSOL Multiphysics 5.1 software. …”

Section: Bi-phasic Formulationmentioning

confidence: 99%

Bi‐phasic theory vs. volumetric viscoelasticity for modelling the behaviour of thin collagenous membranes

Stracuzzi

Ehret

2016

Proc Appl Math and Mech

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Poroelastic materials reinforced by statistically oriented fibres--numerical implementation and application to articular cartilage

Cited by 63 publications

References 0 publications

A poroplastic model of structural reorganisation in porous media of biomechanical interest

A poroplastic model of structural reorganisation in porous media of biomechanical interest

Material description of fluxes in terms of differential forms

Bi‐phasic theory vs. volumetric viscoelasticity for modelling the behaviour of thin collagenous membranes

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