Buckling of an Elastic Ridge: Competition between Wrinkles and Creases.

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 ϕ below a critical value ϕ^{⋆}≈90°, experiments reveal an extended sinusoidal mode, while for ϕ above ϕ^{⋆}, 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 ϕ≤ϕ^{⋆}, as well as the associated critical strain ε_{c}(ϕ). The experimental transition at ϕ^{⋆} is found to occur when this critical strain ε_{c}(ϕ) attains the value ε_{c}(ϕ^{⋆})=0.44 corresponding to the threshold of the subcritical 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.