Modeling shear banding lipid monolayer collapse with finite element analysis

Lipid monolayers are important self-assembled structures in organs like the ears, eyes, and lungs. Mechanisms of related biological processes can be probed through studying the response of lipid monolayers to lateral compressive stress. This is experimentally observed at the air-water interface using a Langmuir trough. Fluorescence microscopy (FM) captures surface morphology which, in the case of biphasic systems, follows coexisting phases: condensed domains within a more expanded matrix. More generally, the lipid monolayer has been thought to be represented as an elastic sheet as far as its mechanical response is concerned. In this sense, it has been observed that lipid monolayers respond to stress through different modes of collapse. Some monolayers relax stress through out-of-plane deformation, while others through in-plane rearrangements of condensed domains, known as shear banding. These collapse modes are accessible by tuning system softness (Carotenuto, et al, 2021), leading to the search for a constitutive material model with similar tunability. An elastic model has been successful in capturing out-of-plane collapse (Diamant, et al, 2001; Lee, 2008; Pocivavsek, et al, 2008) but cannot capture in-plane collapse. Integrating solid mechanics and finite element analysis, we have identified that uniaxial compression of a 2D homogeneous sheet leads to shear bands when the material exhibits a non-monotonic stress-strain response. We extend this model to a heterogeneous thin sheet, built from the domain-matrix morphology of experimental FM images in mixed lipid systems that exhibit biphasic behavior. The simulation results show that we can trigger shear banding in the matrix, allowing for the domains to reorganize and reproduce the morphology as seen in experimental shear banding lipid monolayers. Our findings expand understanding of lipid monolayer response to compression, with the long-term goal of predicting and modeling collapse based on material properties.