royalsocietypublishing.org/journal/rspa Research Cite this article: Auddya D, Zhang X, Gulati R, Vasan R, Garikipati K, Rangamani P, Rudraraju S. 2021 Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhof–Love kinematics and revealed by a three-dimensional computational framework. Proc. R. Soc. A 477: 20210246. https://doi.org/10.1098/rspa.2021.0246 Received: 13 April 2021 Accepted: 11 October 2021 Subject Areas: cellular biophysics, computational mechanics, biomechanics Keywords: biomembranes, Kirchhof-Love, endocytosis, FEM, isogeometric analysis, non-axisymmetric Author for correspondence: Shiva Rudraraju e-mail: shiva.rudraraju@wisc.edu † Both these authors contributed equally. Electronic supplementary material is available online at https://doi.org/10.6084/m9.fgshare. c.5672457. Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhof–Love kinematics and revealed by a three-dimensional computational framework Debabrata Auddya 1, † , Xiaoxuan Zhang 2, † , Rahul Gulati 1 , Ritvik Vasan 5 , Krishna Garikipati 2,3,4 , Padmini Rangamani 5 and Shiva Rudraraju 1 1 Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA 2 Department of Mechanical Engineering, 3 Department of Mathematics, and 4 Michigan Institute for Computational Discovery and Engineering, University of Michigan, Ann Arbor, MI 48109, USA 5 Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093, USA XZ, 0000-0002-0844-5712; SR, 0000-0002-8313-0198 Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while 2021 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited. Downloaded from https://royalsocietypublishing.org/ on 11 November 2021