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 $\varphi$ below a critical value ${\varphi }^{\star }\approx 90^{\circ }$ experiments reveal an extended sinusoidal mode, while for $\varphi$ above ${\varphi }^{\star }$ 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 $\varphi \le {\varphi }^{\star }$, as well as the associated critical strain ${\epsilon }_{\mathrm{c}}(\varphi )$. The experimental transition at ${\varphi }^{\star }$ is found to occur when this critical strain ${\epsilon }_{\mathrm{c}}(\varphi )$ attains the value ${\epsilon }_{\mathrm{c}}({\varphi }^{\star })=0.44$ 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.