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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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Detalles Bibliográficos
Autores principales: Dharmavaram, Sanjay, Wan, Xinran, Perotti, Luigi E.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9608239/
https://www.ncbi.nlm.nih.gov/pubmed/36295719
http://dx.doi.org/10.3390/membranes12100960
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author Dharmavaram, Sanjay
Wan, Xinran
Perotti, Luigi E.
author_facet Dharmavaram, Sanjay
Wan, Xinran
Perotti, Luigi E.
author_sort Dharmavaram, Sanjay
collection PubMed
description 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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spelling pubmed-96082392022-10-28 A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes Dharmavaram, Sanjay Wan, Xinran Perotti, Luigi E. Membranes (Basel) Article 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. MDPI 2022-09-30 /pmc/articles/PMC9608239/ /pubmed/36295719 http://dx.doi.org/10.3390/membranes12100960 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Dharmavaram, Sanjay
Wan, Xinran
Perotti, Luigi E.
A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes
title A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes
title_full A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes
title_fullStr A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes
title_full_unstemmed A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes
title_short A Lagrangian Thin-Shell Finite Element Method for Interacting Particles on Fluid Membranes
title_sort lagrangian thin-shell finite element method for interacting particles on fluid membranes
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9608239/
https://www.ncbi.nlm.nih.gov/pubmed/36295719
http://dx.doi.org/10.3390/membranes12100960
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