Inserted: 8 may 2018
Last Updated: 8 may 2018
In the 1930s Sadowsky derived an asymptotic theory for narrow ribbons. Generalised Sadowsky theories were recently obtained by the authors as a Gamma-limit from two-dimensional plate models. In the present article, we provide a rigorous derivation of these generalised Sadowsky theories starting from nonlinear three-dimensional elasticity. On a technical level, this involves capturing a contribution to the asymptotic energy functional generated by a nonlinear constraint which is satisfied only approximately. It also involves the construction of fine-scale "corrugations" capable of reaching a bending energy regime which is strictly below that of the original Sadowsky functional.
Keywords: Gamma-convergence, nonlinear elasticity, Sadowsky functional, Elastic ribbons