Abstract
In this work, we present a computational formulation based on continuum mechanics to study the interaction of fluid membranes embedded with semiflexible filaments. This is motivated by systems in membrane biology, such as cytoskeletal networks and protein filaments aiding the cell fission process. We model the membrane as a fluid shell via the Helfrich–Canham energy and the filament as a one-dimensional Cosserat continuum. We assume that the filament is tethered to the surface of the membrane while being allowed to freely float on the surface. The fluidity of the membrane and the novel filament-membrane coupling gives rise to unique computational challenges, which are addressed in this work. Finally, we present validation results and apply the formulation to several problems inspired by cellular biology.
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