Browsing by Author "Barchiesi, Marco"

Now showing 1 - 3 of 3
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    A bridging mechanism in the homogenisation of brittle composites with soft inclusions
    (SISSA, 2015) Barchiesi, Marco; Lazzaroni, Giuliano; Zeppieri, Caterina Ida
    We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised 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 ε to obtain, in the limit as ε tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.
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    Loss of polyconvexity by homogenization: a new example
    (2006-04-18T13:35:02Z) Barchiesi, Marco; Mathematics; Functional Analysis and Applications
    This article is devoted to the study of the asymptotic behavior of the zero-energy deformations set of a periodic nonlinear composite material. We approach the problem using two-scale Young measures. We apply our analysis to show that polyconvex energies are not closed with respect to periodic homogenization. The counterexample is obtained through a rank-one laminated structure assembled by mixing two polyconvex functions with $p$-growth, where $p\geq2$ can be fixed arbitrarily.
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    Multiscale homogenization of convex functionals with discontinuous integrand
    (2005) Barchiesi, Marco; Mathematics; Functional Analysis and Applications
    This article is devoted to obtain the $\Gamma$-limit, as $\epsilon$ tends to zero, of the family of functionals $$F_{\epsilon}(u)=\int_{\Omega}f\Bigl(x,\frac{x}{\epsilon},..., \frac{x}{\epsilon^n},\nabla u(x)\Bigr)dx$$, where $f=f(x,y^1,...,y^n,z)$ is periodic in $y^1,...,y^n$, convex in $z$ and satisfies a very weak regularity assumption with respect to $x,y^1,...,y^n$. We approach the problem using the multiscale Young measures.