Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets

The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology (i) emerges even in zero strain configurations, and (ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key role of branch-point (or "monkey-saddle") singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.Comment: 6 pages, 6 figures. This article supersedes arXiv:1504.0073

Non-universality in Micro-branching Instabilities in Rapid Fracture: the Role of Material Properties

In spite of the apparent similarity of micro-branching instabilities in different brittle materials, we propose that the physics determining the typical length- and time-scales characterizing the post-instability patterns differ greatly from material to material. We offer a scaling theory connecting the pattern characteristics to material properties (like molecular weight) in brittle plastics like PMMA, and stress the fundamental differences with patterns in glass which are crucially influenced by 3-dimensional dynamics. In both cases the present ab-initio theoretical models are still too far from reality, disregarding some fundamental physics of the phenomena.Comment: 4 pages, 6 figures, PRL submitte