# Elastic material

Thursday, May 19, 2011 - 2:30pm - 3:00pm

Robert Schroll (University of Massachusetts)

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 solving the governing equations. Here, we consider the building blocks that make up a wrinkle cascade.

Friday, May 20, 2011 - 11:00am - 12:00pm

Shankar Venkataramani (University of Arizona)

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 sheets reflect geometric incompatibility, that is the non-existence of admissible, sufficiently smooth isometric immersions (zero stretching energy test functions).

Thursday, May 19, 2011 - 9:00am - 10:00am

Alan Newell (University of Arizona)

Many of the challenges of finding the shapes of elastic

surfaces have first cousins in the world of pattern formation.

I will

try to sketch out the connections and explain where there are

similarities and where there are profound differences even

though the

equations and the free energies look much the same. If time

permits,

and with the indulgence of the audience, I shall also tell you

how a

three dimensional version of the ideas give rise to objects,

quarks

surfaces have first cousins in the world of pattern formation.

I will

try to sketch out the connections and explain where there are

similarities and where there are profound differences even

though the

equations and the free energies look much the same. If time

permits,

and with the indulgence of the audience, I shall also tell you

how a

three dimensional version of the ideas give rise to objects,

quarks

Monday, May 16, 2011 - 1:30pm - 2:30pm

Marta Lewicka (Rutgers, The State University Of New Jersey )

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 magnitude, and hence contributing to the stretching energy of the film at a level corresponding to the magnitude of the given external force.

Monday, May 16, 2011 - 10:45am - 11:45am

Robert Kohn (New York University)

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 of the pattern can be explored by examining how the minimum energy scales with the sheet thickness. I will introduce this viewpoint by discussing past work on simpler but related

Wednesday, May 18, 2011 - 10:30am - 11:30am

Benny Davidovitch (University of Massachusetts)

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 under radial tension. This axi-symmetric system seems to be the most elementary, yet nontrivial extension of Euler buckling (that emerges under uniaxial compression).

Monday, May 16, 2011 - 3:00pm - 3:30pm

Peter Bella (New York University)

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 first

mathematically rigorous analysis of such a problem. Since our methods require an explicit understanding of the underlying (convex) relaxed problem, we focus on the wrinkling of an annular sheet loaded in the radial direction [Davidovitch et

mathematically rigorous analysis of such a problem. Since our methods require an explicit understanding of the underlying (convex) relaxed problem, we focus on the wrinkling of an annular sheet loaded in the radial direction [Davidovitch et