On Asymptotic Rigidity and Continuity Problems in Nonlinear Elasticity on Manifolds and Hypersurfaces
Gui-Qiang G. Chen,
Siran Li,
Marshall Slemrod
Abstract:Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of elastic bodies for the intrinsic approach to nonlinear elasticity. We first establish a geometric rigidity estimate for mappings from a Riemannian manifold to a sphere (in the spirit of Friesecke-James-Müller [20]), which is the first result of this type for the non-Euclidean… Show more
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