A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes

A recurring motif in soft matter and biophysics is modeling the mechanics of interacting particles on fluid membranes. One of the main outstanding challenges in these applications is the need to model the strong coupling between the substrate deformation and the particles’ positions as the latter fr...

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Bibliographic Details
Published inMembranes (Basel) Vol. 12; no. 10; p. 960
Main Authors Dharmavaram, Sanjay, Wan, Xinran, Perotti, Luigi E.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 30.09.2022
MDPI
Subjects
Analysis
Biophysics
Configurations
Coupling
Deformation
Energy
Equilibrium
Finite element analysis
Finite element method
Formability
Helfrich–Canham model
interacting particles
lipid membranes
Lipids
Mechanics (physics)
Membranes
Methods
model for protein–membrane interaction
Search algorithms
subdivision finite element
Substrates
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Summary:A recurring motif in soft matter and biophysics is modeling the mechanics of interacting particles on fluid membranes. One of the main outstanding challenges in these applications is the need to model the strong coupling between the substrate deformation and the particles’ positions as the latter freely move on the former. This work presents a thin-shell finite element formulation based on subdivision surfaces to compute equilibrium configurations of a thin fluid shell with embedded particles. We use a variational Lagrangian framework to couple the mechanics of the particles and the substrate without having to resort to ad hoc constraints to anchor the particles to the surface. Unlike established methods for such systems, the particles are allowed to move between elements of the finite element mesh. This is achieved by parametrizing the particle locations on the reference configuration. Using the Helfrich–Canham energy as a model for fluid shells, we present the finite element method’s implementation and an efficient search algorithm required to locate particles on the reference mesh. Several analyses with varying numbers of particles are finally presented reproducing symmetries observed in the classic Thomson problem and showcasing the coupling between interacting particles and deformable membranes.
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ISSN:2077-0375
2077-0375
DOI:10.3390/membranes12100960