Journal
MATHEMATICS AND MECHANICS OF SOLIDS
Volume 16, Issue 8, Pages 812-832Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1081286510387233
Keywords
growth; Kirchhoff plates; nonlinear elasticity; residual stress
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Funding
- National Science Foundation [DMS-0907773]
- King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0907773] Funding Source: National Science Foundation
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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.
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