| Author | Edgard S. Almeida and Robert L. Spilker |
|---|---|
| Title | Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part I - Alternate Formulations |
| Year | 1997 |
| Journal | Computer Methods in Biomechanics and Biomedical Engineering |
| Volume | 1 |
| Pages | 25-46 |
| Abstract | This paper addresses finite element-based computational models for the three-dimensional (3-D), nonlinear analysis of soft hydrated tissues, such as the 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 a hyperelastic solid. Alternate mixed-penalty and velocity-pressure finite element formulations are used 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 is discretized in time using an implicit finite difference scheme, and solved using the Newton-Raphson method. Using a discrete divergence operator, an equivalence is shown between the mixed-penalty method and a penalty method previously derived by Suh et al. In Part II, the mixed-penalty and velocity-pressure formulations are used to develop two-dimensional (2-D) quadrilateral and triangular elements and 3-D hexahedral and tetrahedral elements. Numerical examples, including those representative of soft tissue material testing and simple human joints, are used to validate the formulations and to illustrate their applications. A focus of this work is the comparison of alternate formulations for nonlinear problems. While it is demonstrated that both formulations produce a range of converging elements, the velocity-pressure formulation is found to be more efficient computationally. |