# Derivation of a homogenized von Kármán shell theory

@inproceedings{Hornung2012DerivationOA, title={Derivation of a homogenized von K{\'a}rm{\'a}n shell theory}, author={Peter Hornung and Igor Vel{\vc}i{\'c}}, year={2012} }

We derive the model of homogenized von K\'arm\'an shell theory, starting from three dimensional nonlinear elasticity. The original three dimensional model contains two small parameters: the oscillations of the material $\e$ and the thickness of the shell $h$. Depending on the asymptotic ratio of these two parameters, we obtain different asymptotic theories. In the case $h\ll\e$ we identify two different asymptotic theories, depending on the ratio of $h$ and $\e^2$. In the case of convex shells…

## 13 Citations

On the derivation of homogenized bending plate model

- Mathematics, Physics
- 2012

We derive, via simultaneous homogenization and dimension reduction, the $$\Gamma $$Γ-limit for thin elastic plates of thickness $$h$$h whose energy density oscillates on a scale $$\varepsilon…

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- Mathematics, Physics
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- 2016

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- 2013

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Homogenization of bending theory for plates; the case of elastic laminates

- Physics, Mathematics
- 2014

In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the direction of…

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- Mathematics
- 2015

In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the direction of…

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- 2019

In this paper we investigate rods made of nonlinearly elastic, composite–materials that feature a micro-heterogeneous prestrain that oscillates (locally periodic) on a scale that is small compared to…

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- Materials Science
- 2014

In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the thickness direction on…

On effective material parameters of thin perforated shells under static loading

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Abstract One of the defining properties of thin shell problems is that the solution can be viewed as a linear combination of local features, each with its own characteristic thickness-dependent…

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