Nonlinear morphoelastic plates I: Genesis of residual stress

J. McMahon, A. Goriely, M. Tabor

Research output: Contribution to journalArticlepeer-review

8 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 languageEnglish (US)
Pages (from-to)812-832
Number of pages21
JournalMathematics and Mechanics of Solids
Volume16
Issue number8
DOIs
StatePublished - Apr 28 2011
Externally publishedYes

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.

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