Towards predicting shear-banding instabilities in lipid monolayers

Langmuir monolayers are advantageous systems used to investigate how lipid membranes get involved in the physiology of many living structures, such as collapse phenomena in alveolar structures. Much work focuses on characterizing the pressure-bearing capacity of Langmuir films, expressed in the form of isotherm curves. These show that monolayers experience different phases during compression with an according evolution of their mechanical response, incurring into instability events when a critical stress threshold is overcome. Although well-known state equations, which establish an inverse relationship between surface pressure and area change, are able to properly describe monolayer behaviour during liquid expanded phase, the modelling of their nonlinear behaviour in the subsequent condensed region is still an open issue. In this regard, most efforts are addressed to explain out-of-plane collapse by modelling buckling and wrinkling mainly resorting to linearly elastic plate theory. However, some experiments on Langmuir monolayers also show in-plane instability phenomena leading to the formation of the so-called shear bands and, to date, no theoretical description of the onset of shear banding bifurcation in monolayers has been yet provided. For this reason, by adopting a macroscopic description, we here study material stability of the lipid monolayers and exploit an incremental approach to find the conditions that kindle shear bands. In particular, by starting from the widely assumed hypothesis that monolayers behave elastically in the solid-like region, in this work a hyperfoam hyperelastic potential is introduced as a new constitutive strategy to trace back the nonlinear response of monolayer response during densification. In this way, the obtained mechanical properties together with the adopted strain energy are successfully employed to reproduce the onset of shear banding exhibited by some lipid systems under different chemical and thermal conditions.