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Constitutive Modeling of the Stress-Stretch Behavior of Membranes Possessing a Triangulated Network Microstructure

Published online by Cambridge University Press:  01 February 2011

Melis Arslan  and
Mary C. Boyce
Melis Arslan
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, U.S.A.
Mary C. Boyce
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, U.S.A.
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Abstract

The mechanical behavior of the membrane of the red blood cell is governed by two primary microstructural features: the lipid bilayer and the underlying spectrin network. The lipid bilayer is analogous to a 2D fluid in that it resists changes to its planar area, yet poses little resistance to planar shear. A skeletal network of spectrin molecules is crosslinked to the lipid bilayer and provides the shear stiffness of the membrane. Here, a continuum level constitutive model of the large stretch behavior of the red blood cell membrane that directly incorporates the microstructure of the spectrin network is developed. The resemblance of the spectrin network to a triangulated network is used to identify a representative volume element (RVE) for the model. A strain energy density function in terms of an arbitrary planar deformation field is proposed using the RVE. Differentiation of the strain energy density function provides expressions for the general multiaxial stress-stretch behavior of the material. The stress-strain behavior of the membrane when subjected to uniaxial loading conditions in different directions is given, showing the capabilities of the proposed microstructurally-detailed constitutive modeling approach in capturing the evolving anisotropic nature of the mechanical behavior.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 874: Symposium l – Structure and Mechanical Behavior of Biological Materials , 2005 , L6.8
Copyright
Copyright © Materials Research Society 2005

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References

1. Evans, E. A., “A New Material Concept for the Red Cell Membrane”, Biophys. J., 13, pp. 926–940 (1973).Google Scholar
2. Skalak, R., Tozeren, A., Zarda, R. P. and Chien, S., “Strain Energy Function of Red Blood Cell Membranes”, Biophys. J., 13, pp. 245–264 (1973).Google Scholar
3. Evans, E. and Mohandas, N., “Mechanical Properties of the Red Cell Membrane in Relation to Molecular Structure and Genetic Effects”, Annu. Rev. Biophys. Biomol. Struct., 23, pp. 787–818 (1994).Google Scholar
4. Discher, D.E., Boey, S.K, and Boal, D.H., “Phase Transitions and Anisotropic Responses of Planar Triangular Nets under Large Deformation”, Physical Review E 55, 4, pp. 4762–4772 (1997).Google Scholar
5. Boey, S.K, Boal, D.H., and Discher, D.E., “Simulations of the Erythrocyte Cytoskeleton at Large Deformation, II. Micropipette Aspiration”, Biophys. J., 75, pp. 1584–1597 (1998).Google Scholar
6. Liu, S., Derick, L. H. and Palek, J., “Visualization of the Hexagonal Lattice in the Erythrocyte Membrane Skeleton”, J. Cell Biol., 104, pp. 527–536 (1987).Google Scholar
7. Boey, S.K., Boal, D.H., and Discher, D.E., “Simulations of the Erythrocyte Cytoskeleton at Large Deformation I. Microscopic Models”, Biophys. J., 75, pp. 1573–1583 (1998).Google Scholar