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arXiv · 2504.15864

The effects of pressure loads in the dimension reduction of elasticity models

Martin Kružík·Filippo Riva
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Abstract

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 K\'arm\'an-type theories, where a nontrivial interplay arises between the elastic energy and the pressure term. 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 $\Gamma$-limit, we conjecture that a similar independence from the pressure term persists in the most flexible membrane regimes.

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Martin Kružík, Filippo Riva. 2025-04-22. The effects of pressure loads in the dimension reduction of elasticity models. https://arxiv.org/abs/2504.15864

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