A finite element method for viscous membranes

The simulation of biological interfaces at the Living Cell scale relies on membrane models that are a combination of a finite–strain elastic part, typically modeling the contribution of a cytoskeleton, and a viscous part that models the contribution of the lipidic bilayer. The motion of these membranes is driven by a shape-dependent energy, modeled by means of the Canham–Helfrich formula or variants thereof. In this article we review the finite element formulation of elastic membranes, and then extend it so as to deal with the viscous behavior of lipidic bilayers. The resulting numerical method, which is easily implemented on codes developed for solid membranes, is assessed on the simulation of dynamical prolate-to-oblate transitions of simplified red blood cells under tweezing.