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Michael Ortiz and Gustavo Gioia showed in the 90s that the complex patterns arising in compressed elastic films can be analyzed within the context of the calculus of variations. Their initial work focused on films partially debonded from the substrate, subject to isotropic compression arising from the difference in thermal expansion coefficients between film and substrate. In the following two decades different geometries have been studied, as for example anisotropic compression. We review recent mathematical progress in this area, focusing on the rich phase diagram of partially debonded films with a lateral boundary condition.
This paper is motivated by the complex blister patterns sometimes seen in thin elastic films on thick, compliant substrates. These patterns are often induced by an elastic misfit which compresses the film. Blistering permits the film to expand locall
In this paper, we study the thin-film limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii-Moriya interaction (DMI). Our analysis includes both a stationary $Gamma$-convergence result for the micromagnetic energy, as we
Experimental data on thin films of cylinder-forming block copolymers (BC) -- free-standing BC membranes as well as supported BC films -- strongly suggest that the local orientation of the BC patterns is coupled to the geometry in which the patterns a
We are concerned with the dimension reduction analysis for thin three-dimensional elastic films, prestrained via Riemannian metrics with weak curvatures. For the prestrain inducing the incompatible version of the Foppl-von Karman equations, we find
We introduce the study of forcing sets in mathematical origami. The origami material folds flat along straight line segments called creases, each of which is assigned a folding direction of mountain or valley. A subset $F$ of creases is forcing if th