Abstract
Lanir (J Biomech. 16(1):1–12, 1983) proposed a structural model for the anisotropic response of fibrous tissues with fiber bundles oriented in space by a continuous orientation distribution. Each fiber bundle was assumed to have the same undulation distribution that characterizes its nonlinear elastic response. Recently, a discrete fiber icosahedron model for fibrous soft tissues has been introduced, which is based on fiber bundles parallel to the six lines that connect opposing vertices of a regular icosahedron. Although the parameters in the icosahedron model can be determined to match experimental data for the anisotropic response of various tissues, the icosahedron model predicts anisotropic response when the weights of the six fiber bundles are equal. This chapter quantifies this undesirable anisotropic response and refers to a new icosahedron model based on a generalized invariant which also matches experimental data and analytically reduces to an isotropic form when the weights of the fiber bundles are equal.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bazant Z, Oh BH. Microplane model for progressive fracture of concrete and rock. J Eng Mech ASCE. 1985;111(4):559–82.
Bazant ZP, Oh BH. Efficient numerical integration on the surface of a sphere. Z Angew Math Mech. 1986;66(1):37–49.
Christensen RM. Mechanics of low density materials. J Mech Phys Solids. 1986;34(6):563–78.
Christensen RM. Sufficient symmetry conditions for isotropy of the elastic moduli tensor. J Appl Mech. 1987;54(4):772–7.
Ehret AE, Itskov M, Schmid H. Numerical integration on the sphere and its effect on the material symmetry of constitutive equations—a comparative study. Int J Numer Methods Eng. 2010;81(2):189–206.
Elata D, Rubin MB. Isotropy of strain energy functions which depend only on a finite number of directional strain measures. J Appl Mech. 1994;61(2):284–9.
Elata D, Rubin MB. A new representation for the strain energy of anisotropic elastic materials with application to damage evolution in brittle materials. Mech Mater. 1995;19(2–3):171–92.
Flynn C, Rubin MB. An anisotropic discrete fibre model based on a generalised strain invariant with application to soft biological tissues. Int J Eng Sci. 2012;60:66–76.
Flynn C, Rubin MB, Nielsen P. A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles. Int J Numer Methods Biomed Eng. 2011;27(11):1793–811.
Itskov M, Ehret AE. A universal model for the elastic, inelastic and active behaviour of soft biological tissues. GAMM-Mitteilungen. 2009;32(2):221–36.
Itskov M, Ehret AE, Dargazany R. A full-network rubber elasticity model based on analytical integration. Math Mech Solids. 2010;15:655–71.
Lanir Y. Constitutive equations for fibrous connective tissues. J Biomech. 1983;16(1):1–12.
Acknowledgments
This research was partially supported by MB Rubin’s Gerard Swope Chair in Mechanics. The authors would also like to acknowledge helpful discussions with A Rubin about the equal area model.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Flynn, C., Rubin, M.B. (2016). Undesirable Anisotropy in a Discrete Fiber Bundle Model of Fibrous Tissues. In: Kassab, G., Sacks, M. (eds) Structure-Based Mechanics of Tissues and Organs. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7630-7_16
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7630-7_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-7629-1
Online ISBN: 978-1-4899-7630-7
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)