Alternate Hybrid, Mixed, and Penalty Finite Element Formulations for the Biphasic Model of Soft Hydrated Tissues

Abstract

It is widely accepted that soft connective tissues such as tendon, ligament, intervertebral disc, articular cartilage, and meniscus, are multiphasic materials, i.e. a mixture of collagen/elastin fibrils, water, glycosaminoglycans, glycoproteins, and cells. Based on this concept, Kenyon (1979) and Simon et al. (1985) used a classical consolidation theory of soil mechanics (Biot, 1962) to describe aortic tissue and intervertebral disk, respectively. As a more rigorous and theoretically versatile approach, Mow et al. (1980) used mixture theory (Truesdell and Toupin, 1960) to describe the deformation of articular cartilage. In their model, called the biphasic theory, Mow et al. assumed that soft hydrated tissue such as cartilage is a mixture of two immiscible constituents: an incompressible solid matrix and an incompressible interstitial fluid. This model has been shown to accurately describe both the stress distribution and interstitial fluid flow within soft hydrated tissue such as cartilage under various loading conditions (Armstrong, et al., 1984; Mow, et al., 1984; Mak, et al., 1987 Hou, et al., 1989).