Peter Bella

Metric-Induced Wrinkling of a Thin Elastic Sheet

We study the wrinkling of a thin elastic sheet caused by a prescribed non-Euclidean metric. This is a model problem for the patterns seen, for example, in torn plastic sheets and the leaves of plants. Following the lead of other authors, we adopt a variational viewpoint, according to which the wrinkling is driven by minimization of an elastic energy subject to appropriate constraints and boundary conditions. We begin with a broad introduction, including a discussion of key examples (some well-known, others apparently new) that demonstrate the overall character of the problem. We then focus on how the minimum energy scales with respect to the sheet thickness

Corrector Estimates for Elliptic Systems with Random Periodic Coefficients

h

Study of Island Formation in Epitaxially Strained Films on Unbounded Domains

h for certain classes of displacements. Our main result is that when deformations are subject to certain hypotheses, the minimum energy is of order

Wrinkling of a thin circular sheet bonded to a spherical substrate

h^{4/3}

Wrinkles as the Result of Compressive Stresses in an Annular Thin Film

h4/3. We also show that when deformations are subject to more restrictive hypotheses, the minimum energy is strictly larger – of order