Preprint
Inserted: 23 apr 2025
Last Updated: 23 apr 2025
Year: 2025
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 Kármán-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.
Keywords: Gamma-convergence, nonlinear elasticity, von Kármán theory, pressure live loads, membranes, Kirchhoff theory
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