A stabilized finite element formulation for liquid shells and its application to lipid bilayers

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• 作者：Roger A. Sauer^a ; ^{sauer@aices.rwth-aachen.de} ; Thang X. Duong^a ; Kranthi K. Mandadapu^b ; ^c ; David J. Steigmann^d
• 关键词：Cell budding ; Cell tethering ; Helfrich energy ; Isogeometric analysis ; Non-linear finite elements ; Non-linear shell theory
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：330
• 期：Complete
• 页码：436-466
• 全文大小：5087 K
• 卷排序：330

文摘

This paper presents a new finite element (FE) formulation for liquid shells that is based on an explicit, 3D surface discretization using C1C1-continuous finite elements constructed from NURBS interpolation. Both displacement-based and mixed displacement/pressure FE formulations are proposed. The latter is needed for area-incompressible material behavior, where penalty-type regularizations can lead to misleading results. In order to obtain quasi-static solutions for liquid shells devoid of shear stiffness, several numerical stabilization schemes are proposed based on adding stiffness, adding viscosity or using projection. Several numerical examples are considered in order to illustrate the accuracy and the capabilities of the proposed formulation, and to compare the different stabilization schemes. The presented formulation is capable of simulating non-trivial surface shapes associated with tube formation and protein-induced budding of lipid bilayers. In the latter case, the presented formulation yields non-axisymmetric solutions, which have not been observed in previous simulations. It is shown that those non-axisymmetric shapes are preferred over axisymmetric ones.