Elasticity in curved topographies: Exact theories and linear approximations.

摘要: 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 and disclinations. In this paper, we present formulation of theory geometries unifies its underlying geometric topological content with the defects. The two different linear approximations widely used literature shown to arise as systematic expansions reference actual space. Taking concrete example two-dimensional crystal, without central disclination, constrained spherical cap, compare exact evaluate their range validity. We conclude some general discussion about universality nonlinear elasticity.