TY - JOUR
T1 - Nonlinear morphoelastic plates I: Genesis of residual stress
AU - McMahon, J.
AU - Goriely, A.
AU - Tabor, M.
N1 - 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.
PY - 2011/4/28
Y1 - 2011/4/28
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/598993
UR - http://journals.sagepub.com/doi/10.1177/1081286510387233
UR - http://www.scopus.com/inward/record.url?scp=81255185832&partnerID=8YFLogxK
U2 - 10.1177/1081286510387233
DO - 10.1177/1081286510387233
M3 - Article
SN - 1081-2865
VL - 16
SP - 812
EP - 832
JO - Mathematics and Mechanics of Solids
JF - Mathematics and Mechanics of Solids
IS - 8
ER -