This talk presents a computational formulation based on continuum mechanics to study the interaction of fluid membranes embedded with semiflexible filaments. We model the membrane as a thin fluid shell and the filament as a Cosserat rod. We assume that the filament is tethered to the membrane's surface while being allowed to float on it freely. The membrane's fluidity and the filament-membrane coupling through tethering give rise to unique computational challenges, which will be discussed.
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