Fluid membrane vesicles in confinement

Kahraman, Osman; Stoop, Norbert; Müller, Martin

doi:10.1088/1367-2630/14/9/095021

Cited by 25 publications

(47 citation statements)

References 66 publications

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“…Physically, it corresponds to a surface tension. The stress and moment components now become (31) which is identical to (28) for q = K g.…”

Section: Area-incompressible Lipid Bilayermentioning

confidence: 99%

“…Under quasi-static conditions, liquid membranes and shells therefore do not provide any resistance to in-plane shear deformations and thus need to be stabilized. Various stabilization methods have been proposed in the past, considering artificial viscosity [40,52], artificial stiffness [28] and normal offsets -either as a projection of the solution (with intermediate mesh update steps) [52], or as a restriction of the surface variation [48]. The instability problem is absent, if shear stiffness is present, e.g.…”

Section: Introductionmentioning

confidence: 99%

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

Sauer

Duong

Mandadapu

et al. 2017

Journal of Computational Physics

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This paper presents a new finite element (FE) formulation for liquid shells that is based on an explicit, 3D surface discretization using C 1 -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.

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“…Physically, it corresponds to a surface tension. The stress and moment components now become (31) which is identical to (28) for q = K g.…”

Section: Area-incompressible Lipid Bilayermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Sauer

Duong

Mandadapu

et al. 2017

Journal of Computational Physics

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“…No rotational or auxiliary variables are needed. They can handle arbitrary mesh topologies. Subdivision surface elements are easily reformulated for other curvature‐based theories. In particular, their applicability in the context of lipid bilayer mechanics was recently demonstrated .…”

Section: Discussionmentioning

confidence: 99%

“…In particular, their applicability in the context of lipid bilayer mechanics was recently demonstrated [79][80][81][82].…”

Section: Discussionmentioning

confidence: 99%

Subdivision shell elements with anisotropic growth

Vetter

Stoop

Jenni

et al. 2013

Numerical Meth Engineering

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SUMMARYA thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff–Love theory of thin shells is derived and extended to allow for arbitrary in‐plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasistatic, elastic limit. Copyright © 2013 John Wiley & Sons, Ltd.

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“…This focus issue comprises studies of artificial swimming mechanisms [1], specific studies and models of the migration of amoebea [2-4], kinetoplastea [5], and algae [6,7]. Beyond the specific properties of individual swimmers, these studies address generic theoretical aspects, for example synchronisation in the last-mentioned chlamydomonas papers, or the emergence of collective effects such as aggregation and pattern formation in systems of self-propelled particles [8,9], or their continuum modeling [10].The focus issue also gathers contributions that consider closely related (or identical) soft-matter phenomenona in animate and inanimate systems, for example anomalous diffusion [11,12] or elastic shape deformations of elastic membranes [13][14][15]. Next to membranes, the cytoskeleton is the crucial meso-scale structure where mechanical self-organization takes place.…”

mentioning

confidence: 99%