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# Buckling of an elastic ridge: competition between wrinkles and creases

Abstract : We investigate the elastic buckling of a triangular prism made of a soft elastomer. A face of the prism is bonded to a stiff slab that imposes an average axial compression. We observe two possible buckling modes which are localized along the free ridge. For ridge angles $\phi$ below a critical value $\phi^\star\approx 90^\circ$ experiments reveal an extended sinusoidal mode, while for $\phi$ above $\phi^\star$ we observe a series of creases progressively invading the lateral faces starting from the ridge. A numerical linear stability analysis is set up using the finite-element method and correctly predicts the sinusoidal mode for $\phi \leq \phi^\star$, as well as the associated critical strain $\epsilon_{\mathrm{c}}(\phi)$. The experimental transition at $\phi^\star$ is found to occur when this critical strain $\epsilon_{\mathrm{c}}(\phi)$ attains the value $\epsilon_{\mathrm{c}}(\phi^\star) = 0.44$ corresponding to the threshold of the sub-critical surface creasing instability. Previous analyses have focused on elastic crease patterns appearing on planar surfaces, where the role of scale-invariance has been emphasized; our analysis of the elastic ridge provides a different perspective, and reveals that scale-invariance is not a sufficient condition for localization.
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https://hal.sorbonne-universite.fr/hal-01502711
Contributor : Corrado Maurini Connect in order to contact the contributor
Submitted on : Thursday, April 6, 2017 - 5:12:45 AM
Last modification on : Wednesday, November 17, 2021 - 12:29:15 PM

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Claire Lestringant, Corrado Maurini, Arnaud Lazarus, Basile Audoly. Buckling of an elastic ridge: competition between wrinkles and creases. Physical Review Letters, American Physical Society, 2017, 118, pp.165501 ⟨10.1103/PhysRevLett.118.165501⟩. ⟨hal-01502711⟩

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