Nonlinear morphoelastic plates II: Exodus to buckled states

Joseph McMahon; Alain Goriely; Michael Tabor

doi:10.1177/1081286510387234

Nonlinear morphoelastic plates II: Exodus to buckled states

Joseph McMahon, Alain Goriely, Michael Tabor

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English (US)
Pages (from-to)	833-871
Number of pages	39
Journal	Mathematics and Mechanics of Solids
Volume	16
Issue number	8
DOIs	https://doi.org/10.1177/1081286510387234
State	Published - Oct 2011

Keywords

Kirchhoff plates
buckling
growth
non-linear elasticity
residual stress

ASJC Scopus subject areas

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

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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.",

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author = "Joseph McMahon and Alain Goriely and Michael Tabor",

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AU - Goriely, Alain

AU - Tabor, Michael

PY - 2011/10

Y1 - 2011/10

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AB - 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.

KW - Kirchhoff plates

KW - buckling

KW - growth

KW - non-linear elasticity

KW - residual stress

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ER -

Nonlinear morphoelastic plates II: Exodus to buckled states

Abstract

Keywords

ASJC Scopus subject areas

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