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

## TL;DR

This study explores how elastic ridges buckle under compression, revealing a transition from sinusoidal wrinkles to creases depending on ridge angle, with predictions validated by experiments and finite-element analysis.

## Contribution

It provides a combined experimental and numerical analysis of buckling modes in elastic ridges, highlighting the transition mechanism and the role of scale-invariance in localization phenomena.

## Key findings

- Sinusoidal buckling mode for ridge angles below 90°
- Transition to creases occurs at a critical strain of 0.44
- Finite-element analysis accurately predicts buckling behavior

## 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.