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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April 2011
Technical Briefs
Coupled Porohyperelastic Mass Transport (PHEXPT) Finite Element Models for Soft Tissues Using ABAQUS
Jonathan P. Vande Geest,
Jonathan P. Vande Geest
Assistant Professor
Department of Aerospace and Mechanical Engineering, Biomedical Engineering Interdisciplinary Program, and BIO5 Institute,
e-mail: jpv1@email.arizona.edu
University of Arizona
, Tucson, AZ 85721
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B. R. Simon,
B. R. Simon
Department of Aerospace and Mechanical Engineering and Biomedical Engineering Interdisciplinary Program,
University of Arizona
, Tucson, AZ 85721
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Paul H. Rigby,
Paul H. Rigby
Department of Aerospace and Mechanical Engineering,
University of Arizona
, Tucson, AZ 85721
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Tyler P. Newberg
Tyler P. Newberg
Department of Aerospace and Mechanical Engineering,
University of Arizona
, Tucson, AZ 85721
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Jonathan P. Vande Geest
Assistant Professor
Department of Aerospace and Mechanical Engineering, Biomedical Engineering Interdisciplinary Program, and BIO5 Institute,
University of Arizona
, Tucson, AZ 85721e-mail: jpv1@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
Department of Aerospace and Mechanical Engineering,
University of Arizona
, Tucson, AZ 85721
Tyler P. Newberg
Department of Aerospace and Mechanical Engineering,
University of Arizona
, Tucson, AZ 85721J Biomech Eng. Apr 2011, 133(4): 044502 (7 pages)
Published Online: February 18, 2011
Article history
Received:
March 12, 2010
Revised:
January 13, 2011
Posted:
January 20, 2011
Published:
February 18, 2011
Online:
February 18, 2011
Citation
Vande Geest, J. P., Simon, B. R., Rigby, P. H., and Newberg, T. P. (February 18, 2011). "Coupled Porohyperelastic Mass Transport (PHEXPT) Finite Element Models for Soft Tissues Using ABAQUS." ASME. J Biomech Eng. April 2011; 133(4): 044502. https://doi.org/10.1115/1.4003489
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