Marco Barchiesi

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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(More)
In this article we show that for the homogenization of multiple integrals, the quasiconvexification of the cell formula is different from the asymptotic formula in general. To this aim, we construct three examples in three different settings: the homogenization of a discrete model, the homogenization of a composite material and the homogenization of a(More)
We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period ε of the grid and the ratio δ between the thickness of the fibers and the period ε. We show that the asymptotic behavior as(More)
We define a class of deformations in W (Ω,R), p > n−1, with positive Jacobian that do not exhibit cavitation. We characterize that class in terms of the non-negativity of the topological degree and the equality Det = det (that the distributional determinant coincides with the pointwise determinant of the gradient). Maps in this class are shown to satisfy a(More)