KAUST Grant NumberKUK-C1-013-04
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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.
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.
SponsorsThis 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).