Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons

We consider a two-dimensional model of viscoelastic von K\'arm\'an plates in the Kelvin's-Voigt's rheology derived from three-dimensional at finite-strain setting. As width plate goes to zero, we perform dimension-reduction 2D 1D and identify an effective one-dimensional for ribbon comprising stretching, bending, twisting both elastic viscous stress. Our arguments rely on abstract theory gradient flows metric spaces by Sandier Serfaty complement $\Gamma$-convergence analysis K\'{a}rm\'{a}n ribbons [Freddi et al., 2018]. Besides convergence flows, also show associated time-discrete approximations, provide corresponding commutativity result.