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  • Letter
  • Open Access

Stretching and bending of very thick elastic beams

Shiheng Zhao (赵世恒) and Pierre A. Haas*

  • *Contact author: haas@pks.mpg.de
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Phys. Rev. E 114, L053501 – Published 5 November, 2026

DOI: https://doi.org/10.1103/tpd1-t6d2

Abstract

The mechanical energy of an elastic beam separates into stretching and bending energies. This is a result for asymptotically thin beams, but it is often a surprisingly accurate approximation for thick beams, too. Here, we address this conundrum: We compute the deformations of a very thick elastic beam resulting from imposed, asymptotically small deformations of its midline to discover effective stretching and bending moduli. They soften with increasing beam thickness, but, strikingly, their ratio remains approximately constant. In this way, our calculations provide a justification for applying the picture of stretching and bending to thick elastic objects such as biological cell sheets.

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Phys. Rev. E 114, L053501– Published 5 November, 2026
  • Received 1 June 2026
  • Accepted 20 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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