A Linear Viscoelastic Biphasic Model for Soft Tissues Based on the Theory of Porous Media

[+] Author and Article Information
Wolfgang Ehlers, Bernd Markert

Institute of Applied Mechanics (Civil Engineering), University of Stuttgart, Stuttgart, Germany

J Biomech Eng 123(5), 418-424 (Apr 25, 2001) (7 pages) doi:10.1115/1.1388292 History: Received November 30, 1999; Revised April 25, 2001
Copyright © 2001 by ASME
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REV of cartilage with real microstructure consisting of a collagen–proteoglycan matrix saturated with interstitial fluid 18 and biphasic TPM macro model. The initial volume fractions, i.e., solidity and porosity, for cartilage are approximately n0SS=0.25 and n0SF=0.75.
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Variation of the Darcy permeability parameter kF versus the compressive volumetric strain εV for different values of κ. The initial values n0SS=0.25,n0SF=0.75, and k0F=2.17×10−11 m/s are average values of human patellar cartilage.
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Generalized Maxwell model: σESEQSNEQS denotes the solid extra stress with the equilibrium part σEQS and the nonequilibrium part σNEQS=ΣσnSS=(εSe)n+(εSi)n is the corresponding solid strain.
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Discretization with triangles or tetrahedrals
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Definition of initial boundary value problems: (a) Infinitesimal torsion test. A cylindrical sample (h=1.5 mm,d=6.0 mm) is twisted by a jump to φ0=0.126 rad equal to a shear strain of 2.0 percent. (b) Hydrostatic compression test. A cubic specimen (a=3.0 mm) is charged displacement driven with a compressive volumetric strain εV=−5percent within 5.0 s. (c) Axisymmetric indentation test. An axisymmetric disc (h=3.5 mm,r=7.0 mm) is loaded displacement driven about 5.0 percent of height within 5.0 s with a porous permeable indenter (ri=1.0 mm).
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Tangential displacement (left) and torsional moment of the computed infinitesimal torsion test (right). Squares mark the time steps of the time-adaptive computation.
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Pore-fluid pressure and seepage velocity (arrows) after 5.0×106 seconds of the computed consolidation process of the hydrostatic compression test
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Progression of hydrostatic pressure for short (left) and long time scales (right). Squares mark the time steps of the time-adaptive computation.
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The left figure shows the influence of the deformation dependent permeability on the computed indenter reaction force. The right figure shows the decreasing influence of the skeleton viscoelasticity by increasing the loading time from 5.0 s up to 250 s.




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