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Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed-hybrid finite element solution

Kamyar Malakpoor;  Enrique F. Kaasschieter;  Jacques M. Huyghe — 2007

ESAIM: Mathematical Modelling and Numerical Analysis

The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory [J.M. Huyghe and J.D. Janssen, (1997) 793–802; K. Malakpoor, E.F. Kaasschieter and J.M. Huyghe, Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part I: Modeling of incompressible charged porous media. (2007) 661–678]. This theory results in a coupled system of nonlinear parabolic differential equations together with an algebraic constraint...

Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part I: Modelling of incompressible charged porous media

Kamyar Malakpoor;  Enrique F. Kaasschieter;  Jacques M. Huyghe — 2007

ESAIM: Mathematical Modelling and Numerical Analysis

The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory in which a deformable and charged porous medium is saturated with a fluid with dissolved ions. Four components are defined: solid, liquid, cations and anions. The aim of this paper is the construction of the Lagrangian model of the four-component system. It is shown that, with the choice of Lagrangian description of the solid skeleton, the motion of the other components can be described in terms of...

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