Nonlinear morphoelastic plates I: Genesis of residual stress

J. McMahon; A. Goriely; M. Tabor

doi:10.1177/1081286510387233

Nonlinear morphoelastic plates I: Genesis of residual stress

J. McMahon, A. Goriely, M. Tabor

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

10 Scopus citations

Abstract

Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established. © SAGE Publications 2011.

Original language	English (US)
Pages (from-to)	812-832
Number of pages	21
Journal	Mathematics and Mechanics of Solids
Volume	16
Issue number	8
DOIs	https://doi.org/10.1177/1081286510387233
State	Published - Apr 28 2011
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This work was supported by the National Science Foundation (grant number DMS-0907773). AG also gratefully acknowledges partial support from the King Abdullah University of Science and Technology (KAUST) (Award No. KUK-C1-013-04).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Access to Document

10.1177/1081286510387233

Cite this

@article{a5699b5ec9c64c1ea6659b70cde8537a,

title = "Nonlinear morphoelastic plates I: Genesis of residual stress",

abstract = "Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established. {\textcopyright} SAGE Publications 2011.",

author = "J. McMahon and A. Goriely and M. Tabor",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This work was supported by the National Science Foundation (grant number DMS-0907773). AG also gratefully acknowledges partial support from the King Abdullah University of Science and Technology (KAUST) (Award No. KUK-C1-013-04). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2011",

month = apr,

day = "28",

doi = "10.1177/1081286510387233",

language = "English (US)",

volume = "16",

pages = "812--832",

journal = "Mathematics and Mechanics of Solids",

issn = "1081-2865",

publisher = "SAGE Publications",

number = "8",

}

TY - JOUR

T1 - Nonlinear morphoelastic plates I: Genesis of residual stress

AU - McMahon, J.

AU - Goriely, A.

AU - Tabor, M.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This work was supported by the National Science Foundation (grant number DMS-0907773). AG also gratefully acknowledges partial support from the King Abdullah University of Science and Technology (KAUST) (Award No. KUK-C1-013-04). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2011/4/28

Y1 - 2011/4/28

N2 - Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established. © SAGE Publications 2011.

AB - Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established. © SAGE Publications 2011.

UR - http://hdl.handle.net/10754/598993

UR - http://journals.sagepub.com/doi/10.1177/1081286510387233

UR - http://www.scopus.com/inward/record.url?scp=81255185832&partnerID=8YFLogxK

U2 - 10.1177/1081286510387233

DO - 10.1177/1081286510387233

M3 - Article

SN - 1081-2865

VL - 16

SP - 812

EP - 832

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

IS - 8

ER -

Nonlinear morphoelastic plates I: Genesis of residual stress

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this