Computing the volume enclosed by a periodic surface and its variation to model a follower pressure

Mohammad Rahimi, Kuan Zhang, Marino Arroyo

Research output: Contribution to journalArticle

Abstract

In modeling and numerically implementing a follower pressure in a geometrically nonlinear setting, one needs to compute the volume enclosed by a surface and its variation. For closed surfaces, the volume can be expressed as a surface integral invoking the divergence theorem. For periodic systems, widely used in computational physics and materials science, the enclosed volume calculation and its variation is more delicate and has not been examined before. Here, we develop simple expressions involving integrals on the surface, on its boundary lines, and point contributions. We consider two specific situations, a periodic tubular surface and a doubly periodic surface enclosing a volume with a nearby planar substrate, which are useful to model systems such as pressurized carbon nanotubes, supported lipid bilayers or graphene. We provide a set of numerical examples, which show that the familiar surface integral term alone leads to an incorrect volume evaluation and spurious forces at the periodic boundaries.

Original languageEnglish (US)
Pages (from-to)519-525
Number of pages7
JournalComputational Mechanics
Volume55
Issue number3
DOIs
StatePublished - Jan 1 2015

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Computing
Surface integral
Divergence theorem
Lipid Bilayer
Materials Science
Model
Graphene
Periodic Systems
Nanotubes
Lipid bilayers
Carbon
Time varying systems
Materials science
Substrate
Physics
Closed
Numerical Examples
Carbon nanotubes
Line
Evaluation

Keywords

  • Follower load
  • Periodic surface
  • Pressure
  • Volume

Cite this

Computing the volume enclosed by a periodic surface and its variation to model a follower pressure. / Rahimi, Mohammad; Zhang, Kuan; Arroyo, Marino.

In: Computational Mechanics, Vol. 55, No. 3, 01.01.2015, p. 519-525.

Research output: Contribution to journalArticle

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