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Hybrid and mixed‐penalty finite elements for 3‐D analysis of soft hydrated tissue
Author(s) -
Vermilyea M. E.,
Spilker R. L.
Publication year - 1993
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.1620362408
Subject(s) - finite element method , soft tissue , mathematics , penalty method , materials science , computer science , mathematical optimization , structural engineering , engineering , medicine , surgery
Solution of biomechanics problems involving three‐dimensional (3‐D) behaviour of soft tissue on geometries representative of such tissue in vivo will require the use of numerical methods. Toward this end, a pair of tetrahedral finite elements has been developed. The equations which are used to model the tissue behaviour for both elements are those commonly known as the linear biphasic equations. This model assumes that hydrated soft tissue is a mixture of two incompressible, immiscible phases, and employs mixture theory to derive governing equations for its mechanical behaviour. The finite element techniques applied to these equations for the two elements are the mixed‐penalty method and the hybrid method. Both elements are described here, and the special requirements for 3‐D analysis are discussed. Results obtained by solving canonical problems in two and three dimensions using both elements are presented and compared. Both elements are found to produce excellent results. The hybrid element is also noted to have advantages for non‐linear analyses involving finite deformation which will require solution in the future.