Mixed finite element modelling of cartilaginous tissues

E. F. Kaasschieter; A. J.H. Frijns; J. M. Huyghe

doi:10.1016/S0378-4754(02)00105-2

Mixed finite element modelling of cartilaginous tissues

E. F. Kaasschieter, A. J.H. Frijns, J. M. Huyghe

Eindhoven University of Technology

Research output: Contribution to journal › Conference article › peer-review

Abstract

Swelling and shrinking of cartilaginous tissues is modelled by a four-component mixture theory. This theory results in a set of coupled non-linear partial differential equations for the electrochemical potentials and the displacement. For the sake of local mass conservation these equations are discretised in space by a mixed finite element method. Integration in time by backward Euler leads to a non-linear system of algebraic equations. A subtle solution strategy for this system is proposed and tested for one-dimensional situations.

Original language	English
Pages (from-to)	549-560
Number of pages	12
Journal	Mathematics and Computers in Simulation
Volume	61
Issue number	3-6
DOIs	https://doi.org/10.1016/S0378-4754(02)00105-2
Publication status	Published - 30 Jan 2003
Externally published	Yes
Event	MODELLING 2001 - Second IMACS Conference on Mathematical Model - Pilsen, Czech Republic Duration: 25 Jun 2001 → 29 Jun 2001

Keywords

Cartilaginous tissues
Darcy
Electrochemical potentials
Fick
Hooke
Mixed finite elements

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10.1016/S0378-4754(02)00105-2

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title = "Mixed finite element modelling of cartilaginous tissues",

abstract = "Swelling and shrinking of cartilaginous tissues is modelled by a four-component mixture theory. This theory results in a set of coupled non-linear partial differential equations for the electrochemical potentials and the displacement. For the sake of local mass conservation these equations are discretised in space by a mixed finite element method. Integration in time by backward Euler leads to a non-linear system of algebraic equations. A subtle solution strategy for this system is proposed and tested for one-dimensional situations.",

keywords = "Cartilaginous tissues, Darcy, Electrochemical potentials, Fick, Hooke, Mixed finite elements",

author = "Kaasschieter, \{E. F.\} and Frijns, \{A. J.H.\} and Huyghe, \{J. M.\}",

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TY - JOUR

T1 - Mixed finite element modelling of cartilaginous tissues

AU - Kaasschieter, E. F.

AU - Frijns, A. J.H.

AU - Huyghe, J. M.

PY - 2003/1/30

Y1 - 2003/1/30

N2 - Swelling and shrinking of cartilaginous tissues is modelled by a four-component mixture theory. This theory results in a set of coupled non-linear partial differential equations for the electrochemical potentials and the displacement. For the sake of local mass conservation these equations are discretised in space by a mixed finite element method. Integration in time by backward Euler leads to a non-linear system of algebraic equations. A subtle solution strategy for this system is proposed and tested for one-dimensional situations.

AB - Swelling and shrinking of cartilaginous tissues is modelled by a four-component mixture theory. This theory results in a set of coupled non-linear partial differential equations for the electrochemical potentials and the displacement. For the sake of local mass conservation these equations are discretised in space by a mixed finite element method. Integration in time by backward Euler leads to a non-linear system of algebraic equations. A subtle solution strategy for this system is proposed and tested for one-dimensional situations.

KW - Cartilaginous tissues

KW - Darcy

KW - Electrochemical potentials

KW - Fick

KW - Hooke

KW - Mixed finite elements

UR - https://www.scopus.com/pages/publications/0037472543

U2 - 10.1016/S0378-4754(02)00105-2

DO - 10.1016/S0378-4754(02)00105-2

M3 - Conference article

AN - SCOPUS:0037472543

SN - 0378-4754

VL - 61

SP - 549

EP - 560

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

IS - 3-6

T2 - MODELLING 2001 - Second IMACS Conference on Mathematical Model

Y2 - 25 June 2001 through 29 June 2001

ER -

Mixed finite element modelling of cartilaginous tissues

Abstract

Keywords

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