Emmanuel Siéfert, Etienne Reyssat, José Bico and Benoît Roman
Origami-inspired design of Gaussian morphing
fabrics structures. Superimposed flat and inextensible fabric sheets are
heat-sealed along a specific pattern of lines. Upon inflation, this
network of tubular cavities deploys into a large, stiff and light shell,
with a programmed shape.
A detailed article in JMPS « Geometry and mechanics of inextensible curvilinear balloons« on the shape of inextensible curvilinear balloon obtained when sealing along their edges two identical flat pieces of intextensible membranes.
Mylar balloons are popular in funfairs or birthday parties. Their conception is very simple: two pieces of flat thin sheets are cut and sealed together along their edges to form a flat envelope. Inflation tends to deform this envelope in order to maximize its inner volume. However, although thin sheets are easy to bend and hardly resist compressive loads, they barely stretch, which imposes non-trivial geometrical constraints. Such thin sheets are generally described under the framework of “tension field theory” where their stiffness is considered as infinite under stretching and vanishes under compression or bending.
In this study, we focus on the shape after inflation of flat, curved templates of constant width. Counter-intuitively, the curvatures of the paths tend to increase upon inflation, which leads to out of plane buckling of non-confined closed structures. After determining the optimal cross section of axisymmetric annuli, we predict the change in local curvature induced in open paths. We finally describe the location of wrinkled and smooth areas observed in inflated structures that correspond to compression and tension, respectively.
We report a new oscillatory propagation of cracks in thin films where three cracks interact mediated by two delamination fronts. Experimental observations indicate that delamination fronts joining the middle crack to the lateral crack tips swap contact periodically with the crack tip of the middle crack. A model based on a variational approach analytically predicts the condition of propagation and geometrical features of three parallel cracks. The stability conditions and oscillating propagation are found numerically and the predictions are in favorable agreement with experiments. We found that the physical mechanism selecting the wavelength structure is a relaxation process in which the middle crack produces a regular oscillatory path.
We have shown that the spiraling path (when a cone is pushed through a brittle sheet) and the oscillatory crack path (when a blunt object tears through a brittle sheet) both result from the same instability.
Cutting a brittle thin sheet with a blunt object leaves an oscillating crack that seemingly violates the principle of local symmetry for fracture. We experimentally find that at a critical value of a well chosen control parameter the straight propagation is unstable and leads to an oscillatory pattern whose amplitude and wavelength grow by increasing the control parameter. We propose a simple model that unifies this instability with a related problem, namely that of a perforated sheet, where through a similar bifurcation a series of radial cracks spontaneously spiral around each other. We argue that both patterns originate from the same instability.