Rigorous derivation of nonlinear plate theory and geometric rigidity

Gero Friesecke; Stefan Müller; Richard D. James

doi:10.1016/S1631-073X(02)02133-7

Rigorous derivation of nonlinear plate theory and geometric rigidity

Translated title of the contribution: Rigorous derivation of nonlinear plate theory and geometric rigidity

Gero Friesecke, Stefan Müller, Richard D. James

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

63 Scopus citations

Abstract

We show that nonlinear plate theory arises as a Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps ν : (0, 1)³ → ℝ³. We show that the L² distance of ∇ν from a single rotation is bounded by a multiple of the L² distance from the set SO(3) of all rotations.

Translated title of the contribution	Rigorous derivation of nonlinear plate theory and geometric rigidity
Original language	English
Pages (from-to)	173-178
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	334
Issue number	2
DOIs	https://doi.org/10.1016/S1631-073X(02)02133-7
State	Published - 30 Jan 2002
Externally published	Yes

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title = "Rigorous derivation of nonlinear plate theory and geometric rigidity",

abstract = "We show that nonlinear plate theory arises as a Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps ν : (0, 1)3 → ℝ3. We show that the L2 distance of ∇ν from a single rotation is bounded by a multiple of the L2 distance from the set SO(3) of all rotations.",

author = "Gero Friesecke and Stefan M{\"u}ller and James, {Richard D.}",

note = "Funding Information: Acknowledgements. RDJ thanks AFOSR/MURI (F49620-98-1-0433), ARO (DAAG55-98-1-0335), NSF (DMS-0074043) and ONR (N00014-99-1-0925) for supporting his work. GF and SM were partially supported by the TMR network FMRX-CT98-0229.",

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AU - Friesecke, Gero

AU - Müller, Stefan

AU - James, Richard D.

N1 - Funding Information: Acknowledgements. RDJ thanks AFOSR/MURI (F49620-98-1-0433), ARO (DAAG55-98-1-0335), NSF (DMS-0074043) and ONR (N00014-99-1-0925) for supporting his work. GF and SM were partially supported by the TMR network FMRX-CT98-0229.

PY - 2002/1/30

Y1 - 2002/1/30

N2 - We show that nonlinear plate theory arises as a Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps ν : (0, 1)3 → ℝ3. We show that the L2 distance of ∇ν from a single rotation is bounded by a multiple of the L2 distance from the set SO(3) of all rotations.

AB - We show that nonlinear plate theory arises as a Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps ν : (0, 1)3 → ℝ3. We show that the L2 distance of ∇ν from a single rotation is bounded by a multiple of the L2 distance from the set SO(3) of all rotations.

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U2 - 10.1016/S1631-073X(02)02133-7

DO - 10.1016/S1631-073X(02)02133-7

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 2

ER -

Rigorous derivation of nonlinear plate theory and geometric rigidity

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