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3D FE implementation of an incompressible quadriphasic mixture model
Author(s) -
van Loon R.,
Huyghe J. M.,
Wijlaars M. W.,
Baaijens F. P. T.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.723
Subject(s) - discretization , linearization , finite element method , galerkin method , mathematics , compressibility , newton's method , consolidation (business) , interpolation (computer graphics) , lagrange polynomial , weighting , method of mean weighted residuals , mathematical analysis , nonlinear system , computer science , mechanics , physics , thermodynamics , accounting , quantum mechanics , polynomial , acoustics , business , animation , computer graphics (images)
A quadriphasic mixture model, intended to apply to biological tissues, consists of a deforming solid saturated with a fluid, cations and anions. Governing equations of the model are briefly given. The coupled set of differential equations are solved in a finite element method using a weighted residual approach (updated Lagrange). A Newton–Raphson iteration scheme is applied for linearization of the non‐linear set of equations. Interpolation functions are chosen equal to the weighting functions (Galerkin) in discretization. The FE model is then validated for small deformations using the analytical solutions for 1D confined consolidation and swelling. The 3D effects are shown in a swelling cylindrical hydrogel sample. Copyright © 2003 John Wiley & Sons, Ltd.