Biological tissues are typically constituted of dispersed fibers. Modeling the constitutive laws of such tissues remains a challenge. Direct integration over all fibers is considered to be accurate but requires very expensive numerical integration. A general structure tensor (GST) model was previously developed to bypass this costly numerical integration step, but there are concerns about the model's accuracy. Here we estimate the approximation error of the GST model. We further reveal that the GST model ignores strain energy induced by shearing motions. Subsequently, we propose a new characteristic-based constitutive law to better approximate the direct integration model. The new model is very cost-effective and closely approximates the “true” strain energy as calculated by the direct integration when stress–strain nonlinearity or fiber dispersion angle is small.
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July 2016
Research-Article
A Characteristic-Based Constitutive Law for Dispersed Fibers
Liang Ge
Liang Ge
Department of Surgery,
University of California San Francisco,
San Francisco Veterans Affairs Medical Center,
San Francisco, CA 94121
e-mail: liang.ge@va.gov
University of California San Francisco,
San Francisco Veterans Affairs Medical Center,
San Francisco, CA 94121
e-mail: liang.ge@va.gov
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Liang Ge
Department of Surgery,
University of California San Francisco,
San Francisco Veterans Affairs Medical Center,
San Francisco, CA 94121
e-mail: liang.ge@va.gov
University of California San Francisco,
San Francisco Veterans Affairs Medical Center,
San Francisco, CA 94121
e-mail: liang.ge@va.gov
Manuscript received December 3, 2015; final manuscript received April 21, 2016; published online June 7, 2016. Assoc. Editor: Hai-Chao Han.
J Biomech Eng. Jul 2016, 138(7): 071006 (8 pages)
Published Online: June 7, 2016
Article history
Received:
December 3, 2015
Revised:
April 21, 2016
Citation
Ge, L. (June 7, 2016). "A Characteristic-Based Constitutive Law for Dispersed Fibers." ASME. J Biomech Eng. July 2016; 138(7): 071006. https://doi.org/10.1115/1.4033517
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