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• W2954964462 abstract "Almost all available results in elasticity on curved topographies are obtained within either a small curvature expansion or an empirical covariant generalization that accounts for screening between Gaussian curvature and disclinations. In this paper, we present a formulation of elasticity theory in curved geometries that unifies its underlying geometric and topological content with the theory of defects. The two different linear approximations widely used in the literature are shown to arise as systematic expansions in reference and actual space. Taking the concrete example of a 2D crystal, with and without a central disclination, constrained on a spherical cap, we compare the exact results with different approximations and evaluate their range of validity. We conclude with some general discussion about the universality of non-linear elasticity." @default.
• W2954964462 created "2019-07-12" @default.
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• W2954964462 date "2019-06-26" @default.
• W2954964462 modified "2023-10-04" @default.
• W2954964462 title "Elasticity in curved topographies: Exact theories and linear approximations" @default.
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• W2954964462 doi "https://doi.org/10.1103/physreve.99.063005" @default.
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