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

We consider a two-dimensional model of viscoelastic von Kármán plates in the Kelvin’s-Voigt’s rheology derived from a three-dimensional model at a finite-strain setting in Friedrich and Kružík (Arch Ration Mech Anal 238: 489–540, 2020). As the width of the plate goes to zero, we perform a dimension-reduction from 2D to 1D and identify an effective one-dimensional model for a viscoelastic ribbon comprising stretching, bending, and twisting both in the elastic and the viscous stress. Our arguments rely on the abstract theory of gradient flows in metric spaces by Sandier and Serfaty (Commun Pure Appl Math 57:1627–1672, 2004) and complement the $$\Gamma $$ Γ -convergence analysis of elastic von Kármán ribbons in Freddi et al. (Meccanica 53:659–670, 2018). Besides convergence of the gradient flows, we also show convergence of associated time-discrete approximations, and we provide a corresponding commutativity result.

Vibrational dynamics in 2D crystal lattices of borophene

Vibration dynamics of crystalline borophene is considered in the framework of the Born–von Karman model. The vibrations perpendicular to the plane of 2D borophen lattice (flexural modes) are studied.

SOME FEATURED OPTIMAL LAY-UP SOLUTIONS FOR COMPOSITE VAT PLATES UNDER BUCKLING, POSTBUCKLING AND LARGE-DEFLECTION POSTBUCKLING CONDITIONS

The paper is devoted to some featured lay-up solutions for optimized composite VAT plates under such conditions as buckling, postbuckling (within the von Karman limits) or large-deflection postbuckling (beyond the von Karman limits). The corresponding optimality conditions are theoretically analyzed. The possible locally orthotropic solutions are identified and discussed.