Nonlinear morphoelastic plates I: Genesis of residual stress

Joseph McMahon, Alain Goriely, Michael Tabor

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)812-832
Number of pages21
JournalMathematics and Mechanics of Solids
Volume16
Issue number8
DOIs
StatePublished - Oct 1 2011

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Keywords

  • Kirchhoff plates
  • growth
  • nonlinear elasticity
  • residual stress

ASJC Scopus subject areas

  • Mathematics(all)
  • Materials Science(all)
  • Mechanics of Materials

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