Many of the challenges of finding the shapes of elasticsurfaces have first cousins in the world of pattern formation.I willtry to sketch out the connections and explain where there aresimilarities and where there are profound differences eventhough theequations and the free energies look much the same. If timepermits,and with the indulgence of t...
Creator:
Newell, Alan C. (University of Arizona)
Created:
2011-05-19
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Several features, such as d-cones, minimal ridges, developable patches, and collapsed compressive stress, occur regularly in the the configuration of elastic sheets. We dub such features 'building blocks.' By understanding the shape of an elastic sheet as an amalgamation of these building blocks, we can understand its behavior without fully solv...
Creator:
Schroll, Robert (University of Massachusetts)
Created:
2011-05-19
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Thin elastic sheets are usually modeled by variational problems for an energy with two scales, a (strong) stretching energy and a (weak) bending energy. A useful paradigm in understanding the behavior of theses sheets under various loadings/boundary conditions is the following -- Singularites/microstructure in the observed configurations of thin...
Creator:
Venkataramani, Shankar (University of Arizona)
Created:
2011-05-20
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk we will discuss how the mechanical response of an elastic film is affected by subtle geometric properties of its mid-surface. The crucial role is played by spaces of weakly regular (Sobolev) isometries or infinitesimal isometries. These are the deformations of the mid-surface preserving its metric up to a certain prescribed order of...
Creator:
Lewicka, Marta (Rutgers, The State University Of New Jersey)
Created:
2011-05-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Wrinkling is a fundamental mechanism for the relief of compressive stress in thin elastic sheets. It is natural to consider wrinkling as a (supercritical) instability of an appropriate flat, highly-symmetric state of the sheet. This talk will address the subtlety of this approach by considering wrinkling in the Lame` geometry: an annular sheet u...
Creator:
Davidovitch, Benny (University of Massachusetts)
Created:
2011-05-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
It is well known that elastic sheets loaded in tension will wrinkle, with the length scale of wrinkles tending to zero with vanishing thickness of the sheet [Cerda and Mahadevan, Phys. Rev. Lett. 90, 074302 (2003)]. We give the firstmathematically rigorous analysis of such a problem. Since our methods require an explicit understanding of the und...
Creator:
Bella, Peter (New York University)
Created:
2011-05-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The mechanics of a thin elastic sheet can be explored variationally, by minimizing the sum of 'membrane' and 'bending' energy. For some loading conditions, the minimizer develops increasingly fine-scale wrinkles as the sheet thickness tends to 0. While the optimal wrinkle pattern is probably available only numerically, the qualitative features o...
Creator:
Kohn, Robert V. (New York University)
Created:
2011-05-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
