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

摘要

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 giveir, showing the capabilities of the proposed microstructurally-detailed constitutive modeling approach in capturing the evolving anisotropic nature of the mechanical behavior.