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<p>We study the dimensional reduction from three to two dimensions in hyperelastic materials subject to a live load, modeled as a constant pressure force. Our results demonstrate that this loading has a significant impact in higher-order scaling regimes, namely those associated with von Kármán-type theories, where a nontrivial interplay between the elastic energy and the pressure term arises. In contrast, we rigorously show that in lower-order bending regimes, as described by Kirchhoff-type theories, the pressure load does not influence the minimizers. Finally, after identifying the corresponding <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation>-limit, we conjecture that a similar independence from the pressure term persists in the most flexible membrane regimes.</p>

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The Effects of Pressure Loads in the Dimension Reduction of Elasticity Models

  • 期刊论文

  • 发表日期：

    2026年4月3日

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  • Martin Kružík,
  • Filippo Riva

摘要

We study the dimensional reduction from three to two dimensions in hyperelastic materials subject to a live load, modeled as a constant pressure force. Our results demonstrate that this loading has a significant impact in higher-order scaling regimes, namely those associated with von Kármán-type theories, where a nontrivial interplay between the elastic energy and the pressure term arises. In contrast, we rigorously show that in lower-order bending regimes, as described by Kirchhoff-type theories, the pressure load does not influence the minimizers. Finally, after identifying the corresponding \(\Gamma \) Γ -limit, we conjecture that a similar independence from the pressure term persists in the most flexible membrane regimes.