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Article Dans Une Revue Journal of the Mechanics and Physics of Solids Année : 2023

Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: A macroscopic analog of thermodynamic phase transition

Pedro Reis
Basile Audoly

Résumé

We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are separated by so-called perversions (phase boundaries). This instability cannot be described by classical rod theory, which incorporates pre-stress through effective natural curvature and twist; these are both zero due to the mirror symmetry of the pre-stress. Using dimension reduction, we derive a one-dimensional (1D) `rod-like' model from a plate theory, which accounts for inhomogeneous pre-stress as well as finite rotations. The 1D model successfully captures the qualitative features of torsional buckling under a prescribed end-to-end displacement and rotation, including the co-existence of buckled phases possessing opposite twist, and is in good quantitative agreement with the results of numerical (finite-element) simulations and model experiments on elastomeric samples. Our model system provides a macroscopic analog of phase separation and pressure-volume-temperature state diagrams, as described by the classical thermodynamic theory of phase transitions.
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Dates et versions

hal-04199692 , version 1 (08-09-2023)

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Michael Gomez, Pedro Reis, Basile Audoly. Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: A macroscopic analog of thermodynamic phase transition. Journal of the Mechanics and Physics of Solids, 2023, 181, pp.105420. ⟨10.1016/j.jmps.2023.105420⟩. ⟨hal-04199692⟩
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