Simple Transport Analyses Using a Multiphasic Material

Overview

FEBio’s multiphasic material and analysis module were developed to accommodate a host of complex behaviors that may be found in biological tissues, including solute and solvent transport, osmotic effects, solid matrix deformation, chemical reactions, etc. To accommodate these complex behaviors, FEBio uses the “effective fluid pressure” and “effective solute concentration” as nodal variables. These are related to the actual “fluid pressure” and “solute concentration” via relations described in the User’s Manual.

However, in some cases, users may be interested in conducting a simple solute transport analysis without worrying about these complex behaviors. One option is to use the FEBioChem plugin. Alternatively, one can use a multiphasic analysis that can be suitably simplified to analyze a solute transport problem without these added complexities.

Simplifying Steps

1. In the multiphasic material, set the osmotic_coefficient material to type “osm-coef-const” and set its value to 0. This will eliminate osmotic effects.
2. Fix the x,y,z-displacement components of the entire multiphasic domain to zero. (In FEBioStudio, use ‘Select nodes’ and ‘Select backfacing’ to rubber-band over the entire domain.) This means that any constitutive model can be used for the solid matrix of the multiphasic material (e.g., neo-Hookean), but this solid matrix will not deform.
3. Similarly, fix the fluid pressure to zero. This means that any constitutive model can be used for the permeability of the multiphasic material (e.g., perm-const-iso), but the solvent will not flow.

By fixing the displacement and pressure degrees of freedom, the only degrees of freedom that remain are those of the solute(s) defined in the multiphasic material. This means that the computational analysis is not burdened by having to solve for solid displacements or effective fluid pressure. The multiphasic analysis only solves for the effective solute concentrations. As usual for a multiphasic analysis, if the solutes are neutrally charged, their effective concentration is the same as their actual concentration.

The attached axisymmetric diffusion problem in a cylindrical disk illustrates this type of analysis (DiffusionNoOsmoticEffects.feb).