Continuum mechanics of a cellular tissue model

Raz Kupferman; Ben Maman; Michael Moshe

doi:10.1016/j.jmps.2020.104085

Continuum mechanics of a cellular tissue model

Raz Kupferman^*, Ben Maman, Michael Moshe

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We consider a two-dimensional cellular vertex model, modeling the mechanics of epithelial tissues. The energy of a planar configuration penalizes deviations in each cell from a reference perimeter P₀ and a reference area A₀. We study the variational limit of this model as the cell size tends to zero, obtaining a continuum variational model. For P₀²/A₀ below a critical threshold, which corresponds to an isoperimetric constraint, the system is residually-stressed—there are no zero-energy states. For P₀²/A₀ above this threshold, the zero-energy states are highly degenerate, allowing in particular for the formation of microstructures, which are not captured by formal long-wavelength expansions.

Original language	American English
Article number	104085
Journal	Journal of the Mechanics and Physics of Solids
Volume	143
DOIs	https://doi.org/10.1016/j.jmps.2020.104085
State	Published - Oct 2020

Bibliographical note

Funding Information:
We thank B. Dacorogna, R. Kohn, C. Maor and F. Rindler for helpful advice. We are grateful to S. Armon for illuminating discussions on the mechanics of Trichoplax Adherence. RK was partially funded by the Israel Science Foundation (Grant No. 1035/17 ). MM was partially funded by the Israel Science Foundation (Grant No. 1441/19 ).

Publisher Copyright:
© 2020

Keywords

Cellular models
Incompatible elasticity
Γ-convergence

Access to Document

10.1016/j.jmps.2020.104085

Cite this

@article{e805d0b4fc954490be99dd0982006786,

title = "Continuum mechanics of a cellular tissue model",

abstract = "We consider a two-dimensional cellular vertex model, modeling the mechanics of epithelial tissues. The energy of a planar configuration penalizes deviations in each cell from a reference perimeter P0 and a reference area A0. We study the variational limit of this model as the cell size tends to zero, obtaining a continuum variational model. For P02/A0 below a critical threshold, which corresponds to an isoperimetric constraint, the system is residually-stressed—there are no zero-energy states. For P02/A0 above this threshold, the zero-energy states are highly degenerate, allowing in particular for the formation of microstructures, which are not captured by formal long-wavelength expansions.",

keywords = "Cellular models, Incompatible elasticity, Γ-convergence",

author = "Raz Kupferman and Ben Maman and Michael Moshe",

note = "Funding Information: We thank B. Dacorogna, R. Kohn, C. Maor and F. Rindler for helpful advice. We are grateful to S. Armon for illuminating discussions on the mechanics of Trichoplax Adherence. RK was partially funded by the Israel Science Foundation (Grant No. 1035/17 ). MM was partially funded by the Israel Science Foundation (Grant No. 1441/19 ). Publisher Copyright: {\textcopyright} 2020",

year = "2020",

month = oct,

doi = "10.1016/j.jmps.2020.104085",

language = "American English",

volume = "143",

journal = "Journal of the Mechanics and Physics of Solids",

issn = "0022-5096",

publisher = "Elsevier Ltd.",

}

TY - JOUR

T1 - Continuum mechanics of a cellular tissue model

AU - Kupferman, Raz

AU - Maman, Ben

AU - Moshe, Michael

N1 - Funding Information: We thank B. Dacorogna, R. Kohn, C. Maor and F. Rindler for helpful advice. We are grateful to S. Armon for illuminating discussions on the mechanics of Trichoplax Adherence. RK was partially funded by the Israel Science Foundation (Grant No. 1035/17 ). MM was partially funded by the Israel Science Foundation (Grant No. 1441/19 ). Publisher Copyright: © 2020

PY - 2020/10

Y1 - 2020/10

N2 - We consider a two-dimensional cellular vertex model, modeling the mechanics of epithelial tissues. The energy of a planar configuration penalizes deviations in each cell from a reference perimeter P0 and a reference area A0. We study the variational limit of this model as the cell size tends to zero, obtaining a continuum variational model. For P02/A0 below a critical threshold, which corresponds to an isoperimetric constraint, the system is residually-stressed—there are no zero-energy states. For P02/A0 above this threshold, the zero-energy states are highly degenerate, allowing in particular for the formation of microstructures, which are not captured by formal long-wavelength expansions.

AB - We consider a two-dimensional cellular vertex model, modeling the mechanics of epithelial tissues. The energy of a planar configuration penalizes deviations in each cell from a reference perimeter P0 and a reference area A0. We study the variational limit of this model as the cell size tends to zero, obtaining a continuum variational model. For P02/A0 below a critical threshold, which corresponds to an isoperimetric constraint, the system is residually-stressed—there are no zero-energy states. For P02/A0 above this threshold, the zero-energy states are highly degenerate, allowing in particular for the formation of microstructures, which are not captured by formal long-wavelength expansions.

KW - Cellular models

KW - Incompatible elasticity

KW - Γ-convergence

UR - http://www.scopus.com/inward/record.url?scp=85087938569&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2020.104085

DO - 10.1016/j.jmps.2020.104085

M3 - Article

AN - SCOPUS:85087938569

SN - 0022-5096

VL - 143

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

M1 - 104085

ER -

Continuum mechanics of a cellular tissue model

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this