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Article Dans Une Revue Journal of the Mechanics and Physics of Solids Année : 2020

Geometry and mechanics of inextensible curvilinear balloons

Résumé

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.
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Dates et versions

hal-03015308 , version 1 (19-11-2020)

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Emmanuel Siéfert, José Bico, Etienne Reyssat, Benoît Roman. Geometry and mechanics of inextensible curvilinear balloons. Journal of the Mechanics and Physics of Solids, 2020, 143, pp.104068. ⟨10.1016/j.jmps.2020.104068⟩. ⟨hal-03015308⟩
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