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 two-dimensional fluid in that it resists changes to its surface area, yet poses little resistance to shear. A skeletal network of spectrin molecules is cross-linked to the lipid bilayer and provides the shear stiffness of the membrane. Here, a general 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 triangulated structure of the spectrin network is used to identify a representative volume element (RVE) for the model. A strain energy density function is constructed using the RVE together with various representations of the underlying molecular chain force-extension behaviors where the chain extensions are kinematically determined by the macroscopic deformation gradient. Expressions for the nonlinear finite deformation stress-strain behavior of the membrane are obtained by proper differentiation of the strain energy function. The stress-strain behaviors of the membrane when subjected to tensile and simple shear loading in different directions are obtained, demonstrating the capabilities of the proposed microstructurally detailed constitutive modeling approach in capturing the small to large strain nonlinear, anisotropic mechanical behavior. The sources of nonlinearity and evolving anisotropy are delineated by simultaneous monitoring of the evolution in microstructure including chain extensions, forces and orientations as a function of macroscopic stretch. The model captures the effect of pretension on the mechanical response where pretension is found to increase the initial modulus and decrease the limiting extensibility of the networked membrane.
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July 2006
Technical Papers
Constitutive Modeling of the Finite Deformation Behavior of Membranes Possessing a Triangulated Network Microstructure
M. Arslan,
M. Arslan
Department of Mechanical Engineering,
Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology
, Cambridge, MA
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M. C. Boyce
M. C. Boyce
Fellow ASME
Department of Mechanical Engineering,
Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology
, Cambridge, MA
Search for other works by this author on:
M. Arslan
Department of Mechanical Engineering,
Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology
, Cambridge, MA
M. C. Boyce
Fellow ASME
Department of Mechanical Engineering,
Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology
, Cambridge, MAJ. Appl. Mech. Jul 2006, 73(4): 536-543 (8 pages)
Published Online: September 30, 2005
Article history
Received:
May 17, 2005
Revised:
September 30, 2005
Citation
Arslan, M., and Boyce, M. C. (September 30, 2005). "Constitutive Modeling of the Finite Deformation Behavior of Membranes Possessing a Triangulated Network Microstructure." ASME. J. Appl. Mech. July 2006; 73(4): 536–543. https://doi.org/10.1115/1.2130360
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