### 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 language | English (US) |
---|---|

Pages (from-to) | 519-525 |

Number of pages | 7 |

Journal | Computational Mechanics |

Volume | 55 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2015 |

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### Keywords

- Follower load
- Periodic surface
- Pressure
- Volume

### Cite this

*Computational Mechanics*,

*55*(3), 519-525. https://doi.org/10.1007/s00466-014-1119-9

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

Research output: Contribution to journal › Article

*Computational Mechanics*, vol. 55, no. 3, pp. 519-525. https://doi.org/10.1007/s00466-014-1119-9

}

TY - JOUR

T1 - Computing the volume enclosed by a periodic surface and its variation to model a follower pressure

AU - Rahimi, Mohammad

AU - Zhang, Kuan

AU - Arroyo, Marino

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

KW - Follower load

KW - Periodic surface

KW - Pressure

KW - Volume

UR - http://www.scopus.com/inward/record.url?scp=84925488339&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925488339&partnerID=8YFLogxK

U2 - 10.1007/s00466-014-1119-9

DO - 10.1007/s00466-014-1119-9

M3 - Article

AN - SCOPUS:84925488339

VL - 55

SP - 519

EP - 525

JO - Computational Mechanics

JF - Computational Mechanics

SN - 0178-7675

IS - 3

ER -