The scale and nature of sulcification patterns

Details The scale and nature of sulcification patterns The scale and nature of sulcification patterns

2011-11-07

arxiv.org/abs/1111.1494v2

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 2 figures; new title and abstract; clarification of the role of pre-stress following Eq. 5

Scientific paper

Sulci are ubiquitous surface folds in soft elastomers which can nucleate when the lateral compression exceeds a critical value. Here we develop a near threshold, post-nucleation theory of this instability consistent with our finite element computations. Our theory reveals sulcification to be a new kind of first order solid-solid phase transition between a uniformly strained featureless elastic phase and a localized elastic phase, an isolated sulcus in a half-space, but with arbitrary size. We show that sufficiently strained finite size bodies have an uncountable number of extrema indexed by the almost arbitrary positions of sulci, and that these sulci grow, like gas bubbles in a fluid, by a simple scaling transformation with increasing compression. However, the strain at each sulcus remains pinned at a critical value while the sulcus grows. Furthermore, we show that depending on the boundary conditions, sulcus formation can arise either as a sub-critical or a super-critical bifurcation in a thick, supported, compressed slab, thus generalizing the classical Euler buckling instability in thin elastic systems. More generally, our theory for the onset and formation of localized sulci has implications for patterns based on energy minimization principles in systems that are scale invariant, or nearly so; examples include cavitation, fracture etc..

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