Generalized Sadowsky Theory For Ribbons From Three-Dimensional Nonlinear Elasticity – Roberto Paroni (Universita’ di Pisa)

Venue

Sala Seminari (Dip. Matematica).

Abstract

In the 1930s Sadowsky derived an asymptotic theory for narrow ribbons. We here provide a rigorous derivation of the generalized Sadowsky theory starting from nonlinear three-dimensional elasticity by means of Γ-convergence. 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 that is strictly below that of the original Sadowsky functional. The talk is based on a joint work with L. Freddi, P. Hornung, and M.G. Mora.

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