Soft Nucleation of an Elastic Crease

Creasing instability is ubiquitous in soft solids; however, its inception remains enigmatic as it cannot be captured by the standard linearization techniques. It also does not fit the conventional picture of a barrier-crossing nucleation, and instead carries some features of a second order phase transition. Here we show that despite its fundamentally nonlinear nature, creasing has its origin in marginal stability which is, however, obscured by the dominance of long-range elastic interactions. We argue that despite its supercritical (soft) character, creasing bifurcation can be identified by the condition that the (generalized) driving force acting on an incipient stress singularity degenerates. The analytic instability criterion, obtained in this way, shows an excellent agreement with both physical experiments and direct numerical simulations.

Figure 1

Sketch of the (a) reference and (b) actual configurations of a creased elastic slab subjected to a compressive stretch $\lambda$ in the horizontal direction. The blue line indicates the (material) path $\gamma$ used to compute the energy flux. Shaded areas show the internal solution. An inset in (b) illustrates the critical deformed shape (intermediate asymptotics) obtained analitically for the neo-Hookean material with a crease with a self-contact length $\delta \ell \ll L$.

Figure 2

Stability limits: creasing threshold (this Letter)—blue; Biot threshold—red, inextensible limit—black. Squares: FEM simulations [49].