| Author | Edgard S. Almeida and Robert L. Spilker |
|---|---|
| Title | An Evaluation of Mixed and Penalty Biphasic Elements Using the Linear Confined Compression Problem |
| Year | 1997 |
| Abstract | This paper evaluates finite elements for the three-dimensional (3-D) analysis of soft hydrated tissues such as articular cartilage in diarthrodial joints under physiologically relevant loading conditions. A biphasic continuum description is used to represent the soft tissue as a two-phase mixture of incompressible inviscid fluid and an incompressible solid. Alternate mixed-penalty and velocity-pressure finite element formulations have been developed to solve the nonlinear biphasic governing equations, including the effects of a strain-dependent permeability and a hyperelastic solid phase under finite deformation. The resulting first-order nonlinear system of equations are discretized in time using an implicit finite difference scheme, and solved using the Newton-Raphson method. As a precursor to nonlinear analysis the mixed-penalty and velocity-pressure formulations are used here to evaluate two-dimensional (2-D) quadrilateral and triangular elements and 3-D hexahedral and tetrahedral elements for use in linear biphasic problems. The confined compression problem, while one-dimensional in nature, provides a demanding numerical example for evaluation of the convergence characteristics of a range of elements. The purpose of this study is to provide such a comparison as a guide to nonlinear analysis. |