Constitutive Modeling of the Stress-Stretch Behavior of Two-Dimensional Triangulated Macromolecular Networks Containing Folded Domains

The mechanical behavior of the red blood cell membrane is governed by the lipid bilayer which resists changes in surface area and the underlying spectrin network which resists changes in shape. The constituent spectrin chains of the network consist of a series of domains along the chain, which exhibit noncovalent interactions. Upon sufficient extension of a chain, each folded domain undergoes mechanically-induced unfolding after reaching a chain force between 10 and $35pN$⁠. Individual spectrin chains within the network experience their first unfolding event at different levels of macroscopic strain depending on the macroscopic loading conditions and the orientation of each constituent chain with respect to the macroscopic loading. A microstructurally-informed continuum level constitutive model is developed which tracks individual chain deformation behavior as well as the overall macroscopic network stress-strain behavior. Using the introduced continuum approach and statistical mechanics based models of the chain force-extension behavior together with a transition state model of domain unfolding; a constitutive model for the membrane stress-stretch behavior is constructed. Uniaxial tension and simple shear behaviors of the membrane are simulated incorporating the unfolding of the individual chains. A Taylor averaging approach is used as a first approximation to account for the irregularities in the spectrin network which result in a near plateau-like force behavior with increasing stretch.