Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Snap buckling of bistable beams under combined mechanical and magnetic loading

Arefeh Abbasi

Arefeh Abbasi

Flexible Structures Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland

Contribution: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing

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Tomohiko G. Sano

Tomohiko G. Sano

Flexible Structures Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland

Department of Mechanical Engineering, Keio University, Yokohama, Kanagawa, 2230061, Japan

Contribution: Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Writing – original draft, Writing – review & editing

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Dong Yan

Dong Yan

Flexible Structures Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland

Contribution: Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Writing – original draft, Writing – review & editing

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Pedro M. Reis

Pedro M. Reis

Flexible Structures Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland

[email protected]

Contribution: Conceptualization, Investigation, Methodology, Supervision, Writing – original draft, Writing – review & editing

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Published:https://doi.org/10.1098/rsta.2022.0029

    We investigate the mechanics of bistable, hard-magnetic, elastic beams, combining experiments, finite-element modelling (FEM) and a reduced-order theory. The beam is made of a hard magneto-rheological elastomer, comprising two segments with antiparallel magnetization along the centreline, and is set into a bistable curved configuration by imposing an end-to-end shortening. Reversible snapping is possible between these two stable states. First, we experimentally characterize the critical field strength for the onset of snapping, at different levels of end-to-end shortening. Second, we perform three-dimensional FEM simulations using the Riks method to analyse high-order deformation modes during snapping. Third, we develop a reduced-order centreline-based beam theory to rationalize the observed magneto-elastic response. The theory and simulations are validated against experiments, with an excellent quantitative agreement. Finally, we consider the case of combined magnetic loading and poking force, examining how the applied field affects the bistability and quantifying the maximum load-bearing capacity. Our work provides a set of predictive tools for the rational design of one-dimensional, bistable, magneto-elastic structural elements.

    This article is part of the theme issue ‘Probing and dynamics of shock sensitive shells’.

    Footnotes

    One contribution of 13 to a theme issue ‘Probing and dynamics of shock sensitive shells’.

    Electronic supplementary material is available online at https://doi.org/10.6084/m9.figshare.c.6373197.

    References