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We show that nonlinearly elastic plates of thickness h→0 with an ε -periodic structure such that ε−2h→0 exhibit non-standard behaviour in the asymptotic two-dimensional reduction from three-dimensional elasticity: in general, their effective stored-energy density is “discontinuously anisotropic” in all directions. The proof relies on a new result concerning an additional isometric constraint that deformation fields must satisfy on the microscale.
|Number of pages||39|
|Journal||Calculus of Variations and Partial Differential Equations|
|Early online date||13 Nov 2015|
|Publication status||Published - 1 Dec 2015|
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- 1 Finished
23/07/14 → 22/06/19
Project: Research council