Nonlinear morphoelastic plates I: Genesis of residual stress

J. McMahon, A. Goriely, M. Tabor

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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
Issue number8
StatePublished - Apr 28 2011
Externally publishedYes


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