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A mixed finite element formulation of triphasic mechano‐electrochemical theory for charged, hydrated biological soft tissues
Author(s) -
Sun D. N.,
Gu W. Y.,
Guo X. E.,
Lai W. M.,
Mow V. C.
Publication year - 1999
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/(sici)1097-0207(19990810)45:10<1375::aid-nme635>3.0.co;2-7
Subject(s) - finite element method , electrochemistry , materials science , biological tissue , mechanics , classical mechanics , biomedical engineering , biological system , physics , chemistry , electrode , thermodynamics , engineering , biology
An equivalent new expression of the triphasic mechano‐electrochemical theory [9] is presented and a mixed finite element formulation is developed using the standard Galerkin weighted residual method. Solid displacement u s , modified electrochemical/chemical potentials ϵ w , ϵ + and ϵ − (with dimensions of concentration) for water, cation and anion are chosen as the four primary degrees of freedom (DOFs) and are independently interpolated. The modified Newton–Raphson iterative procedure is employed to handle the non‐linear terms. The resulting first‐order Ordinary Differential Equations (ODEs) with respect to time are solved using the implicit Euler backward scheme which is unconditionally stable. One‐dimensional (1‐D) linear isoparametric element is developed. The final algebraic equations form a non‐symmetric but sparse matrix system. With the current choice of primary DOFs, the formulation has the advantage of small amount of storage, and the jump conditions between elements and across the interface boundary are satisfied automatically. The finite element formulation has been used to investigate a 1‐D triphasic stress relaxation problem in the confined compression configuration and a 1‐D triphasic free swelling problem. The formulation accuracy and convergence for 1‐D cases are examined with independent finite difference methods. The FEM results are in excellent agreement with those obtained from the other methods. Copyright © 1999 John Wiley & Sons, Ltd.