Abstract

Soft solids often exhibit complex deformation patterns under the application of mechanical loads. In this talk, we are motivated by the celebrated Biot problem (1965) of surface instability of an elastic half-space under compression. Using a linear stability analysis, Biot’s work shows that an initially flat surface of a Neo-Hookean solid loses stability to form surface wrinkles at a critical compressive strain. Whereas, recent experiments on rubber blocks under compression report the formation of highly localized creases at a strain well below the strain predicted by Biot’s analysis. To explain this discrepancy, several methods proposed in the existing literature rely on introducing ad-hoc imperfections in the model. Such a trial-and-error approach may or may not succeed; when successful, the results imply that creasing is a local bifurcation from the homogeneous state of deformation, which is known to be false.

Our approach is based on the application of tools in bifurcation theory coupled with path-following numerical continuation. We exploit the inherent symmetry of the system and compute different symmetry-breaking bifurcation paths. We study the stability of the equilibrium configurations on these paths using the criterion of local energy minimization along with Floquet-Bloch theory. We present bifurcation diagrams to show that the highly localized stable creases are not local bifurcations from the homogeneous deformations. They rather evolve as localization of wrinkles along global bifurcation paths far away from the initial instability of the flat state.