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Mixed Finite Elements for the Modeling of Cartilaginous Tissues.

K. Malakpoor

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Project description:

The swelling and shrinking behaviour of cartilaginous tissues can be modelled by a four component mixture theory in which deformable and charged porous medium is saturated with a fluid with dissolved ions. This theory results in a coupled system of non-linear parabolic differential equations together with an algebraic constraint for electroneutrality. The goal of this project is the three-dimensional computational solution of the system of equations. A suitably chosen mixed finite element method fulfils the conservation laws exactly and yields non-oscillatory solutions. This choice should be based on a thorough understanding of the system of equations. Furthermore, a suitable choice for the time-integration is needed as well as an efficient solution procedure for the resulting non-linear equations. The numerical results will be compared with measurements that will be obtained in a related project.

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