ABAQUS-Based, Coupled Porohyperelastic Transport Finite Element Models for Soft Hydrated Biological Structures

General theoretical, experimental, and finite element models (FEMs) based on porous media formulations were developed to study complex normal and pathological mechanical-transport phenomena in biological structures and soft tissues. These continuum models view soft tissues as a solid (fibrous matrix) in which mobile fluid (water) and mobile species (ions, molecules, drugs) are transported during finite deformation. Two specific models were considered, i.e. the mixed porohyperelastic transport swelling (MPHETS) or equivalent porohyperelastic transport swelling (PHETS) [

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] and the “porohypereleastic mass transport (PHEXPT)” ABAQUS models [

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]. The theoretical formulations are the basis for FEMs and identify necessary material property functions. A suite of experiments is described that allows measurement of material parameters (elasticity, permeability, diffusivity, etc). If the PHETS “osmotic coefficient” is relatively small, then a novel partially coupled PHEXPT model can be implemented using an extended version of ABAQUS CAE [

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]. Mathematical relations were identified that relate PHETS and ABAQUS constitutive equations. A specialized FORTRAN program transfers PHE FEM (hyperelastic and pore fluid element) material parameters and transient response (deformation, pore fluid pressure, water flux, etc.) to the mass transport XPT FEM. This second XPT FEM then provides the transient diffusion-convection mass transport solution (concentration, relative species flux, etc.). The extensive capabilities of ABAQUS CAE (finite element library, anisotropic nonlinear materials, automated model generation, inputoutput display, etc.) can be used in PHEXPT simulations of complex soft tissue mechanics where finite deformations are coupled to fluid and species transport. Example applications of this new PHEXPT FEM procedure will include coupled structural-transport in large arteries, (drug eluting) stented arteries, tissue engineered vascular grafts, and the eyeball.