Caterina Ida Zeppieri

Line-Tension Model for Plasticity as the

In this paper we rigorously derive a line-tension model for plasticity as the

\Gamma

\Gamma

-Limit of a Nonlinear Dislocation Energy

-limit of a nonlinear mesoscopic dislocation energy, without resorting to the introduction of an ad hoc cut-off radius. The

Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers

\Gamma

THE NEUMANN SIEVE PROBLEM AND DIMENSIONAL REDUCTION: A MULTISCALE APPROACH

-limit we obtain as the length of the Burgers vector tends to zero has the same form as the

A Bridging Mechanism in the Homogenization of Brittle Composites with Soft Inclusions

\Gamma

Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy

-limit obtained by starting from a linear, semidiscrete dislocation energy. The nonlinearity, however, creates several mathematical difficulties, which we tackled by proving suitable versions of the rigidity estimate in non-simply-connected domains and by performing a rigorous two-scale linearization of the energy around an equilibrium configuration.

Homogenization of fiber reinforced brittle material: the intermediate case

In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields.

Gradient Theory for Geometrically Nonlinear Plasticity via the Homogenization of Dislocations

We perform a multiscale analysis for the elastic energy of a n-dimensional bilayer thin film of thickness 2δ whose layers are connected through an e-periodically distributed contact zone. Describing the contact zone as a union of (n - 1)-dimensional balls of radius r ≪ e (the holes of the sieve) and assuming that δ ≪ e, we show that the asymptotic memory of the sieve (as e → 0) is witnessed by the presence of an extra interfacial energy term. Moreover, we find three different limit behaviors (or regimes) depending on the mutual vanishing rate of δ and r. We also give an explicit nonlinear capacitary-type formula for the interfacial energy density in each regime.

Second-Order Edge-Penalization in the Ambrosio--Tortorelli functional

We provide a homogenization result for the energy-functional associated with a purely brittle composite whose microstructure is characterized by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale