Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response , where is a characteristic dimension, is the elasticity tensor, and is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.
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June 2007
Technical Papers
Equivalence Between Short-Time Biphasic and Incompressible Elastic Material Responses
Gerard A. Ateshian
,
Gerard A. Ateshian
Departments of Mechanical Engineering and Biomedical Engineering,
Columbia University
, New York, NY 10027
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Benjamin J. Ellis
,
Benjamin J. Ellis
Department of Bioengineering and Scientific Computing and Imaging Institute,
University of Utah
, Salt Lake City, UT
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Jeffrey A. Weiss
Jeffrey A. Weiss
Department of Bioengineering and Scientific Computing and Imaging Institute,
University of Utah
, Salt Lake City, UT
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Gerard A. Ateshian
Departments of Mechanical Engineering and Biomedical Engineering,
Columbia University
, New York, NY 10027
Benjamin J. Ellis
Department of Bioengineering and Scientific Computing and Imaging Institute,
University of Utah
, Salt Lake City, UT
Jeffrey A. Weiss
Department of Bioengineering and Scientific Computing and Imaging Institute,
University of Utah
, Salt Lake City, UTJ Biomech Eng. Jun 2007, 129(3): 405-412 (8 pages)
Published Online: November 8, 2006
Article history
Received:
May 18, 2006
Revised:
November 8, 2006
Citation
Ateshian, G. A., Ellis, B. J., and Weiss, J. A. (November 8, 2006). "Equivalence Between Short-Time Biphasic and Incompressible Elastic Material Responses." ASME. J Biomech Eng. June 2007; 129(3): 405–412. https://doi.org/10.1115/1.2720918
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