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Asymptotically exact strain-gradient models for nonlinear slender elastic structures: a systematic derivation method

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Figure 1: Dimension reduction for an abstract slender structure. Left column (a,a’): reference configuration highlighting a particular cross-section with coordinate S
Figure 2: A homogeneous solution with uniform macroscopic strain h: microscopic displacement y h , microscopic strain E h
Figure 3: An axisymmetric membrane: (a) reference and (b) current configurations.
Figure 4: Solutions for a propagating bulge in an axisymmetric membrane with initial aspect ratio L/⇢ = 30: comparison of the predictions of the full axisymmetric membrane model ( § 3.1) and of the reduced model in equation (3.4), from Lestringant and Audo
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