Nonlinear morphoelastic plates II: Exodus to buckled states

Type
Article

Authors
McMahon, J.
Goriely, A.
Tabor, M.

KAUST Grant Number
KUK-C1-013-04

Online Publication Date
2011-05-11

Print Publication Date
2011-11

Date
2011-05-11

Abstract
Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed. © SAGE Publications 2011.

Citation
McMahon J, Goriely A, Tabor M (2011) Nonlinear morphoelastic plates II: Exodus to buckled states. Mathematics and Mechanics of Solids 16: 833–871. Available: http://dx.doi.org/10.1177/1081286510387234.

Acknowledgements
This work was supported by the National Science Foundation under grant DMS-0907773. AG also gratefully acknowledges partial support from Award No. KUK-C1-013-04, made by the King Abdullah University of Science and Technology (KAUST).

Publisher
SAGE Publications

Journal
Mathematics and Mechanics of Solids

DOI
10.1177/1081286510387234

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