arXiv subjects

Federico Cianci

Publications and source records attributed to Federico Cianci.

3 recordsLinked to original sources

arXiv2025

Dimension reduction for time-dependent von Kármán rods

This paper aims to study the convergence of solutions in three-dimensional nonlinear elastodynamics for a thin rod as its cross section shrinks to zero for displacements that are comparable to the small radius of the rod. Assuming the existence of solutions and proper control of the torsional velocity, we show how these converge to the solutions of an effective dimensionally reduced model which is a version of the the time dependent von Kármán equations for a one-dimensional rod. In the presence of high-frequency torsional vibrations, energy can dissipate in the limit and we obtain additional contributions in the limiting equations.

math.AP↗

arXiv2025

Dynamic crack growth in viscoelastic materials with memory

In this paper we introduce a model of dynamic crack growth in viscoelastic material, where the damping term depends on the history of the deformation. The model is based on a dynamic energy dissipation balance and on a maximal dissipation condition. Our main result is an existence theorem in dimension two under some a priori regularity constraints on the cracks.

math.AP↗

arXiv2025

Uniqueness and continuous dependence for a viscoelastic problem with memory in domains with time dependent cracks

We study some hyperbolic partial integro-differential systems in domains with time dependent cracks. In particular, we give conditions on the cracks which imply the uniqueness of the solution with prescribed initial-boundary conditions, and its continuous dependence on the cracks.

math.AP↗