A note on convergence of low energy critical points  
of nonlinear elasticity functionals,  
for thin shells of arbitrary geometry

Marta Lewicka

A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry

Marta Lewicka (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness and around the mid-surface of arbitrary geometry, converge as → 0 to the critical points of the von Kármán functional on , recently proposed in [Lewicka , (to appear)]. This result extends the statement in [Müller and Pakzad, (2008) 1018–1032], derived for the case of plates when $S \subset ℝ^{2}$ . The convergence holds provided the elastic energies of the 3d deformations...

A simple proof of the characterization of functions of low Aviles Giga energy on a ball regularity

Andrew Lorent (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain ⊂ ℝ the functional is $I_{ϵ} (u) = \frac{1}{2} {^{\int}}_{Ω} ϵ^{-1} {|1 - {|Du|}^{2}|}^{2} + ϵ {|D^{2} u|}^{2} d z$ where belongs to the subset of functions in $W_{0}^{2, 2} (Ω)$ whose gradient (in the sense of trace) satisfies ()· = 1 where is...

Displaying similar documents to “A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry”

A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry

A simple proof of the characterization of functions of low Aviles Giga energy on a ball regularity