Ricerc@Sapienza

A novel multiscale strategy is proposed for the damage analysis of masonry structures modeled as periodic composites. Such a computational strategy, whose aim is to reduce the typically high computational cost exhibited by fully microscopic numerical analyses, is based on a multiscale/multidomain model equipped with an adaptive capability, which allows to automatically zoom-in the zones incipiently affected by damage onset.

We prove existence and uniqueness for solutions to equilibrium problems
for free–standing, traction–free, non homogeneous crystals in the presence of plastic
slips. Moreover we prove that this class of problems is closed under G-convergence of
the operators. In particular the homogenization procedure, valid for elliptic systems
in linear elasticity, depicts the macroscopic features of a composite material in the
presence of plastic deformation.

Multiscale periodic homogenization is extended to an Orlicz-
Sobolev setting. It is shown by the reiteraded periodic two-scale convergence
method that the sequence of minimizers of a class of highly oscillatory minimizations
problems involving convex functionals, converges to the minimizers
of a homogenized problem with a suitable convex function.

In the present paper we perform the homogenization of the semilinear elliptic problem
\begin{equation*}
\begin{cases}
u^\eps \geq 0 & \mbox{in} \; \oeps,\\
\displaystyle - div \,A(x) D u^\eps = F(x,u^\eps) & \mbox{in} \; \oeps,\\
u^\eps = 0 & \mbox{on} \; \partial \oeps.\\
\end{cases}
\end{equation*}

Diffusion in inhomogeneous materials can be described by both the Fick and Fokker--Planck diffusion equations.
Here, we study a mixed Fick and Fokker--Planck diffusion problem with coefficients rapidly oscillating both in space and time.
We obtain macroscopic models performing the homogenization limit by means of the unfolding technique.

In this paper, we study the periodic homogenization of the stationary heat equation in
a domain with two connected components, separated by an oscillating interface defined
on prefractal Koch type curves. The problem depends both on the parameter n, which
is the index of the prefractal iteration, and ε, that defines the periodic structure of the
composite material. First, we study the limit as n goes to infinity, giving rise to a limit
problem defined on a domain with fractal interface. Then, we compute the limit as ε

The study of thermal, mechanical and electrical properties of composite materials plays an increasingly important role in material sciences because of their wide spectrum of applica-
tions, for instance, in industrial processes, biomathematics, medical diagnosis. In this talk, we discuss some models which describe the thermal diffusivity or the electrical
conductivity in a composite medium with a nely mixed periodic structure, assuming that the microstructure of the materials under consideration is made by two different diffusive

We study the thermal properties of a composite material in which a periodic array of finely mixed perfect thermal conductors is inserted.
The suitable model describing the behaviour of such physical materials leads to the so-called equivalued surface boundary value problem.
To analyze the overall conductivity of the composite medium (when the size of the inclusions tends to zero),
we make use of the homogenization theory, employing the unfolding technique.

We study, by means of the periodic unfolding technique, the homogenization of a modified bidomain model, which describes the propagation of the action potential in the cardiac electrophysiology. Such a model, allowing the presence of pathological zones in the heart, involves various geometries and non-standard transmission conditions on the interface between the healthy and the damaged part of the cardiac muscle.

We study the overall thermal conductivity of a composite material obtained by inserting in a hosting medium an array of finely mixed inclusions made of perfect heat conductors.
The physical properties of this material are useful in applications and are obtained using the periodic unfolding method.

The peculiarity of this problem calls for a suitable choice of test functions in the unfolding procedure, which leads to a non-standard variational two-scale problem, that cannot be written in a strong form, as usual.