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.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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