Hydrated soft tissue is represented as a mixture of deformable porous solid and interstitial mobile fluid. The solid is assumed to be intrinsically incompressible and hyperelastic, and the fluid is assumed to be intrinsically incompressible and inviscid;​ the effect of fluid viscosity is implicitly incorporated into a diffusive momentum exchange between the two constituents. The governing equations of the biphasic soft tissue under finite deformation are based on mixture theory. A nonlinear constitutive behavior is assumed, and the stress-strain relations are defined in terms of the free energy function. In the present study, an exponential-type free energy function for the nonlinear elasticity of the solid phase is assumed. Nonlinear strain dependent permeability is also assumed.

A finite element model is formulated via a Galerkin weighted residual method coupled with a penalty treatm ent of the in compressibility condition. Using a total Lagrangian formulation, the nonlinear weighted residual statement, expressed with respect to the reference configuration, leads to a coupled nonlinear system of first order differential equations. An unconditionally stable implicit finite difference algorithm is used to obtain a set of temporal response histories. The nonlinear constitutive equation for the solid phase elasticity is incrementally linearized in term s of the second PiolaKirchhoff stress and the corresponding Lagrangian strain. An infinitesimal linear model is used to study the convergence characteristics of the penalty formulation in the biphasic model. A proper set of solution parameters such as mesh size and time increment has been estimated from the analytical solutions or independent finite difference solutions of simple problems, if available.

The nonlinear dynamic finite element model is used to analyze experimental problems with analytically intractable initial and/or boundary conditions. Among those are the confined compression and the unconfined compression problems, with the effect of the frictional adhesion between the tissue specimen and the peripheral surface, and with the effect of nonlinear strain dependent permeability and the finite deformation.