Dynamical Origami

Lay-language version of "Dynamic Oragami"

Presented at the 61st APS Division of Fluid Dynamics Meeting in San Antonio
At 9:57 a.m. on Tuesday, November 25, 2008 in Room 101B of the Gonzales Convention Center
Gray arrow Abstract


Arnaud Antkowiak
Institut J-L-R D’Alembert, CNRS & University Pierre and Marie Curie
Paris, France.

Christophe Josserand
Institut J-L-R D’Alembert, CNRS & University Pierre and Marie Curie,
Paris, France.

Origami is the Japanese name for the art and science of folding. The different structures in traditional Origami have long fascinated biologists, physicists and mathematicians. For instance, physicists see in them the intriguing interactions between geometrical singularities and the elastic properties of materials. Natural examples of folding include bird wings, flower petals, leaves.

Some of the structures are related to growth or packing processes. In industry, examples include the unfolding of solar panel arrays for space satellites and micro-technology devices involving smaller and smaller patterns and structures. Using well-controlled forces at small scales remains thus an important issue.

While the description of origami has been so far mostly limited to equilibrium or quasi-static configurations, in our research we perform the rapid folding of elastic thin sheets. These highly dynamical origami are achieved by means of drop impacts on elastic flat sheet patterns (see figure 1 below and the movie here [PDMS_triangle_trap.mov]).

In this configuration, the driving forces controlling the folding are surface tension and the inertia of the impacting drops. The role of the latter is quite subtle as it first transforms into surface energy during the drops spreading. As a result, the large drop interface increases the efficiency of surface tension and its role in the retraction process.

Figure 1

Figure 1: a drop is impacting a triangular elastic thin sheet (made in PDMS, a polymer). The drop first spreads on the triangular map and then retracts. The elastic sheet is entrained by the interface during retraction and a drop-elastic sheet embedded structure is formed. Because of the impact dyamics, this "dressed" drop finally rebounds.

Changing the drop (its radius or velocity)or the elastic sheet (its thickness or pattern properties allows for a large variety of results: cylindrical shapes, partial or total folding. This rich complexity of dynamical origami has a very interesting consequence: for a given shape of elastic sheet, one can control the folding dynamics by changing the impacting drop characteristics. This shape selection by dynamical process can be observed in figure 2, where the same PDMS sheet can form a cylinder, a 2-fold or a 4-fold structure depending on the impact conditions (see movies here [partial_folding.mov],[cylinder.mov],[pyramidal.mov]).

Figure 2

Figure 2: Illustration of shape selection when a drop impacts on the same elastic pattern. The three situations are characterized by different drop radii and velocities.

Such properties and controls of elastic sheet folding mediated by drop impacts is a potential way of improving micro-processing of small-scale objects. Another promising prospect is the encapsulation of a solidifying liquid by an elastic pattern.