A large strain finite element analysis of cartilage deformation with electrokinetic coupling

Kojić, Miloš; Filipović, Nenad; Mijailovic, Srboljub

doi:10.1016/s0045-7825(00)00246-2

Cited by 9 publications

(10 citation statements)

References 8 publications

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“…Mechanical description of these materials is of utmost importance in many fields of engineering and science. Extensive studies have thus been conducted over the years to advance various mechanical theories of porous media for application to problems in the fields of biomechanics, geotechnical engineering, geophysics, physical chemistry, agricultural engineering, and materials science, among others (Almeida and Spilker, 1998;Atkin and Craine, 1976;Bachmat and Bear, 1986a,b;Bear, 1972;Biot, 1955Biot, , 1956Biot, , 1967Booker, 1974;Borja, 2004Borja, , 2005Bowen, 1976;Carter et al, 1979;Chao et al, 1998;Coussy, 1995;Coussy et al, 1998;Cowin, 1999;de Boer, 2000;Ehlers et al, 2004;Hassanizadeh and Gray, 1979a,b, 1980, 1990Hutter et al, 1999;Huyghe et al, 1991;Knothe-Tate, 2003;Kojic et al, 2001;Levenston et al, 1998;Lewis and Schrefler, 1987;Li et al, 2004;Moreland, 1972;Oettl et al, 2003Oettl et al, , 2004Oettl, 2003;Piekarski and Munro, 1977;Prevost, 1980;Slattery, 1967Slattery, , 1981Spilker et al, 1992;Suh et al, 1991;Taber, 1995;Wei and Muraleetharan, 2002a,b;…”

Section: Introductionmentioning

confidence: 99%

On the mechanical energy and effective stress in saturated and unsaturated porous continua

Borja

2006

International Journal of Solids and Structures

220

172

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This paper has two objectives: (a) to formulate a mechanical theory of porous continua within the framework of strong discontinuity concept commonly employed for the analysis of strain localization in inelastic solids; and (b) to introduce an effective stress tensor for three-phase (solid-water-air) partially saturated porous continua emerging from principles of thermodynamics. To achieve the first objective, strong forms of the boundary-value problems are compared between two formulations, the first in which the velocity jump at the solid-fluid interface is treated as a strong discontinuity problem, and the second in which the strong discontinuity is smeared in the representative volume element. As for the second objective, an effective Cauchy stress tensor of the form r ¼ r þ ð1 À K=K s Þ p1 emerges from the formulation, where r is the total stress tensor, K and K s are the bulk moduli of the solid matrix and solid phase, respectively, and p is the mean pore water and pore air pressures weighted according to the degree of saturation. We show from the first and second laws of thermodynamics that this effective stress tensor is power-conjugate to the solid rate of deformation tensor, and that it includes the mechanical power required to compress the solid phase.

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Section: Introductionmentioning

confidence: 99%

On the mechanical energy and effective stress in saturated and unsaturated porous continua

Borja

2006

International Journal of Solids and Structures

220

172

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“…and resulting fluid flow. With regard to multi-phase continuum formulations in biomechanics, two-and three-field formulations (and more fields when chemical and electrical effects are included) have been used for simulating deformation of soft, hydrated biological tissues, such as cartilage and heart muscle, for small strains [8] and finite strains [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of porous media at finite strain

Borja

Regueiro

2004

Computer Methods in Applied Mechanics and Engineering

132

139

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We present a finite element model for the analysis of a mechanical phenomenon involving dynamic expulsion of fluids from a fully saturated porous solid matrix in the regime of large deformation. Momentum and mass conservation laws are written in Lagrangian form by a pull-back from the current configuration to the reference configuration following the solid matrix motion. A complete formulation based on the motion of the solid and fluid phases is first presented; then approximations are made with respect to the material time derivative of the relative flow velocity vector to arrive at a so-called (v; p)-formulation, which is subsequently implemented in a finite element model. We show how the resulting finite element matrix equations can be consistently linearized, using a compressible neo-Hookean hyperelastic material with a Kelvin solid viscous enhancement for the solid matrix as a test function for the nonlinear constitutive model. Numerical examples are presented demonstrating the significance of large deformation effects on the transient dynamic responses of porous structures, as well as the strong convergence profile exhibited by the iterative algorithm.

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“…In the following analysis we employed the effective stress, σ ′, defined as

which was relevant for the constitutive relations of the solid. Using the definition of relative velocity q as the volume of the fluid passing in a unit time through a unit area of the mixture (Darcy's velocity), we obtained

and transformed ( 6 ) into

The final continuity equation using the elastic constitutive law and fluid incompressibility was given in the form

The resulting FE system of equations was solved incrementally [ 14 ] with a time step Δ t . We imposed the condition that the balance equations are satisfied at the end of each time step ( t + Δ t ).…”

Section: Methodsmentioning

confidence: 99%

“…We imposed the condition that the balance equations are satisfied at the end of each time step ( t + Δ t ). Hence, we derived the following system of equations:

where F u , F p , F q , and F ϕ were forces in the balance equations for displacement, pressure, fluid velocity, and electrical potential, respectively, and m u u and m q u were mass terms in mass matrix [ 14 ].…”

Section: Methodsmentioning

confidence: 99%

Assessment of Knee Cartilage Stress Distribution and Deformation Using Motion Capture System and Wearable Sensors for Force Ratio Detection

Mijailović

Vulović

Milankovic

et al. 2015

Computational and Mathematical Methods in Medicine

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Knowledge about the knee cartilage deformation ratio as well as the knee cartilage stress distribution is of particular importance in clinical studies due to the fact that these represent some of the basic indicators of cartilage state and that they also provide information about joint cartilage wear so medical doctors can predict when it is necessary to perform surgery on a patient. In this research, we apply various kinds of sensors such as a system of infrared cameras and reflective markers, three-axis accelerometer, and force plate. The fluorescent marker and accelerometers are placed on the patient's hip, knee, and ankle, respectively. During a normal walk we are recording the space position of markers, acceleration, and ground reaction force by force plate. Measured data are included in the biomechanical model of the knee joint. Geometry for this model is defined from CT images. This model includes the impact of ground reaction forces, contact force between femur and tibia, patient body weight, ligaments, and muscle forces. The boundary conditions are created for the finite element method in order to noninvasively determine the cartilage stress distribution.

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A large strain finite element analysis of cartilage deformation with electrokinetic coupling

Cited by 9 publications

References 8 publications

On the mechanical energy and effective stress in saturated and unsaturated porous continua

On the mechanical energy and effective stress in saturated and unsaturated porous continua

Dynamics of porous media at finite strain

Assessment of Knee Cartilage Stress Distribution and Deformation Using Motion Capture System and Wearable Sensors for Force Ratio Detection

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