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
N1 - Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2015/3
Y1 - 2015/3
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 -