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Technical Briefs

Coupled Porohyperelastic Mass Transport (PHEXPT) Finite Element Models for Soft Tissues Using ABAQUS

[+] Author and Article Information
Jonathan P. Vande Geest1

Department of Aerospace and Mechanical Engineering, Biomedical Engineering Interdisciplinary Program, and BIO5 Institute, University of Arizona, Tucson, AZ 85721jpv1@email.arizona.edu

B. R. Simon

Department of Aerospace and Mechanical Engineering and Biomedical Engineering Interdisciplinary Program, University of Arizona, Tucson, AZ 85721

Paul H. Rigby, Tyler P. Newberg

Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721

1

Corresponding author.

J Biomech Eng 133(4), 044502 (Feb 18, 2011) (7 pages) doi:10.1115/1.4003489 History: Received March 12, 2010; Revised January 13, 2011; Posted January 20, 2011; Published February 18, 2011; Online February 18, 2011

Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS -based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Time course of small deformation concentration profiles. The dotted line corresponds to the steady state pure diffusion solution while the solid black line corresponds to the steady state diffusion and convection solution. In this plot, ϕ̂ is the molar concentration of the species.

Grahic Jump Location
Figure 2

Solutions for primary field variables and the associated “fluxes” for a flowing confined compression, 1D Terzaghi boundary value problem. In this plot, ϕ̂ is the molar concentration of the species.

Grahic Jump Location
Figure 3

Solutions for primary field variables and their associated fluxes for an axisymmetric pressurized tube. In this plot, ϕ̂ is the molar concentration of the species.

Grahic Jump Location
Figure 4

Jump discontinuity in ABAQUS mass concentration at a material interface. This PHEXPT FEM was run under infinitesimal deformation.

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