Nonlinear morphoelastic plates I: Genesis of residual stress

Handle URI:
http://hdl.handle.net/10754/598993
Title:
Nonlinear morphoelastic plates I: Genesis of residual stress
Authors:
McMahon, J.; Goriely, A.; Tabor, M.
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.
Citation:
McMahon J, Goriely A, Tabor M (2011) Nonlinear morphoelastic plates I: Genesis of residual stress. Mathematics and Mechanics of Solids 16: 812–832. Available: http://dx.doi.org/10.1177/1081286510387233.
Publisher:
SAGE Publications
Journal:
Mathematics and Mechanics of Solids
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
28-Apr-2011
DOI:
10.1177/1081286510387233
Type:
Article
ISSN:
1081-2865; 1741-3028
Sponsors:
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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMcMahon, J.en
dc.contributor.authorGoriely, A.en
dc.contributor.authorTabor, M.en
dc.date.accessioned2016-02-25T13:50:47Zen
dc.date.available2016-02-25T13:50:47Zen
dc.date.issued2011-04-28en
dc.identifier.citationMcMahon J, Goriely A, Tabor M (2011) Nonlinear morphoelastic plates I: Genesis of residual stress. Mathematics and Mechanics of Solids 16: 812–832. Available: http://dx.doi.org/10.1177/1081286510387233.en
dc.identifier.issn1081-2865en
dc.identifier.issn1741-3028en
dc.identifier.doi10.1177/1081286510387233en
dc.identifier.urihttp://hdl.handle.net/10754/598993en
dc.description.abstractVolumetric 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.en
dc.description.sponsorshipThis 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).en
dc.publisherSAGE Publicationsen
dc.subjectgrowthen
dc.subjectKirchhoff platesen
dc.subjectnonlinear elasticityen
dc.subjectresidual stressen
dc.titleNonlinear morphoelastic plates I: Genesis of residual stressen
dc.typeArticleen
dc.identifier.journalMathematics and Mechanics of Solidsen
dc.contributor.institutionUniversity of Arizona, Tucson, United Statesen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.