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<p>This article derives homogenized bending shell theories starting from three-dimensional nonlinear elasticity. The original three-dimensional model contains three small parameters: the two homogenization scales <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10659_2025_10154_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> <EquationSource Format="TEX">$\varepsilon $</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10659_2025_10154_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi>ε</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$\varepsilon ^{2}$</EquationSource> </InlineEquation> of the material properties and the thickness <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10659_2025_10154_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>h</mi> </math></EquationSource> <EquationSource Format="TEX">$h$</EquationSource> </InlineEquation> of the shell. We obtain different limiting behaviors depending on the limit of various ratios of these three parameters.</p>

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Bending Shell Theories for Multiscale Materials from \(3D\) Nonlinear Elasticity

  • 期刊论文

  • 发表日期：

    2025年7月23日

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  • Tiziana Durante,
  • Luisa Faella,
  • Pedro Hernández-Llanos,
  • Ravi Prakash

摘要

This article derives homogenized bending shell theories starting from three-dimensional nonlinear elasticity. The original three-dimensional model contains three small parameters: the two homogenization scales ε $\varepsilon $ and ε 2 $\varepsilon ^{2}$ of the material properties and the thickness h $h$ of the shell. We obtain different limiting behaviors depending on the limit of various ratios of these three parameters.