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TECHNICAL PAPERS: Soft Tissues

A Sub-Domain Inverse Finite Element Characterization of Hyperelastic Membranes Including Soft Tissues

[+] Author and Article Information
Padmanabhan Seshaiyer

Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042

Jay D. Humphrey

Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843-3120

J Biomech Eng 125(3), 363-371 (Jun 10, 2003) (9 pages) doi:10.1115/1.1574333 History: Received April 01, 2002; Revised February 01, 2003; Online June 10, 2003
Copyright © 2003 by ASME
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Figures

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Schema of a general membrane inflation. Panel A shows five markers that can be tracked experimentally using a video system whereas Panel B shows the associated four-element computational “sub-domain” Ωs⊂Ω. The sub-domain can be made as small as allowed experimentally, and can be repeated at multiple locations on the specimen to explore possible material heterogeneities.
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Schema showing a possible four element sub-domain on an inflated sphere (panel A) and an axisymmetrically inflated membrane (panel B). The latter also shows a three noded element used in the forward problem in an axisymmetric finite element solution.
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Results for the inflation of a neo-Hookean spherical membrane as a function of the in-plane stretch λ. The top and middle panels show the material response for moderate stretches, less than that associated with a limit point instability (λ=71/6). The bottom panel shows the estimated value of the neo-Hookean parameter for increasing values of λ, which includes increasing numbers of equilibrium configurations.
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Estimated parameter values versus number of equilibrium configurations for a neo-Hookean sphere inflated to a stretch of 1.33; noise is 0.01 mm.
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Similar to Figure 4 except for a Mooney-Rivlin sphere inflated to a stretch of 1.33 (Γ=0.89); noise is 0.01 mm.
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Similar to Figure 4 except for a Fung-exponential sphere inflated to a stretch of 1.1 (α=0.2,β=1.0); noise is 0.01 mm.
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Estimated parameter values as a function of increasing experimental noise for a neo-Hookean sphere inflated to a stretch of 1.33 via 10 equilibrium configurations.
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Similar to Figure 7 except for a Mooney-Rivlin sphere inflated to a stretch of 1.33 via 10 equilibrium configurations.
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Similar to Figure 7 except for a Fung-exponential sphere inflated to a stretch of 1.05 via 10 equilibrium configurations.
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Estimated parameter values for an orthotropic Fung-exponential material over element 10 (left panels) and over element 17 (right panels). See text for details.

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