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}
}
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13 Citations
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2
Methods Citations
1

13 Citations

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Citation Type

On the derivation of homogenized bending plate model
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Derivation of a homogenized nonlinear plate theory from 3d elasticity
We derive, via simultaneous homogenization and dimension reduction, the $$\Gamma $$Γ-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much…
Non-periodic homogenization of bending–torsion theory for inextensible rods from 3D elasticity
We derive, by means of $$\Gamma $$Γ-convergence, the equations of homogenized bending rod starting from 3D nonlinear elasticity equations. The main assumption is that the energy behaves like…
Homogenization of the nonlinear bending theory for plates
We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of $$\Gamma $$Γ-convergence. In contrast to what one naturally would…
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Starting from 3D elasticity equations we derive the model of the homogenized von K\'arm\'an plate by means of $\Gamma$-convergence. This generalizes the recent results, where the material…
Homogenization of bending theory for plates; the case of elastic laminates
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…
Homogenization of bending theory for plates; the case of oscillations in the direction of thickness
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…
Derivation of a Homogenized Bending–Torsion Theory for Rods with Micro-Heterogeneous Prestrain
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…
General homogenization of bending theory for plates from 3D elasticity; the case of elastic laminates
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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References

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On the derivation of homogenized bending plate model
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 $$\varepsilon…
DERIVATION OF A HOMOGENIZED VON-KÁRMÁN PLATE THEORY FROM 3D NONLINEAR ELASTICITY
We rigorously derive a homogenized von-Karman plate theory as a Γ-limit from nonlinear three-dimensional elasticity by combining homogenization and dimension reduction. Our starting point is an…
The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
SummaryWe consider a shell-like three-dimensional nonlinearly hyperelastic body and we let its thickness go to zero. We show, under appropriate hypotheses on the applied loads, that the deformations…
Derivation of a homogenized nonlinear plate theory from 3d elasticity
We derive, via simultaneous homogenization and dimension reduction, the $$\Gamma $$Γ-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much…
Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity
We discuss the limiting behavior (using the notion of Γ-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the…
A Theorem on Geometric Rigidity and the Derivation of Nonlinear Plate Theory from Three-Dimensional Elasticity
The energy functional of nonlinear plate theory is a curvature functional for surfaces first proposed on physical grounds by G. Kirchhoff in 1850. We show that it arises as a Γ‐limit of…
A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity
Homogenization of linear elastic shells
Homogenization techniques were used by Duvaut (1976,1978) in asymptotic analyse of 3-dimensional periodic continuum problems and periodic von Kármán plates.In this paper we homogenize…
Homogenization, linearization and dimension reduction in elasticity with variational methods
The objective of this thesis is the derivation of effective theories for thin elastic bodies with periodic microstructure. The main result is the rigorous, ansatz free derivation of a homogenized…
Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence
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