Variationally derived 3-field finite element formulations for quasistatic poroelastic analysis of hydrated biological tissues Original Research Article

Hydrated biological tissues are often modeled mechanically as poroelastic media with intrinsically incompressible solid and fluid constituents. Unlike many engineering materials, these tissues may typically experience finite deformations during normal, physiological activities. Accurate and efficient finite element formulations are required to solve large problems of experimental and clinical relevance. This manuscript describes two new 3-field (u-p-W) mixed finite element formulations based on Lagrange multiplier and Augmented Lagrangian representations of the saturation/incompressibility constraint. As a precursor, the continuum mixture theory for finite deformation, quasistatic poroelasticity with constituent incompressibility is first reformulated within the variational framework of the principal of virtual power. In doing so, the equivalence of the continuum mixture theory and Biot formulations for this problem is established. The improved performance of the mixed formulations over an analogous 2-field (u-W) penalty formulation is demonstrated using axisymmetric numerical examples.