00629nas a2200121   4500008004300000245007900043210006900122260002200191520021000213100002100423700002700444856003600471       2010                        en_Ud  00aHomogenization of fiber reinforced brittle material: the intermediate case0 aHomogenization of fiber reinforced brittle material the intermed  bWalter de Gruyter3 aWe derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure.1 aDal Maso, Gianni1 aZeppieri, Caterina Ida  uhttp://hdl.handle.net/1963/360700927nas a2200133   4500008004300000245007300043210006900116520048700185100002100672700001900693700002000712700002500732856003600757       2009                        en_Ud  00aA higher order model for image restoration: the one dimensional case0 ahigher order model for image restoration the one dimensional cas3 aThe higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni1 aMorini, Massimiliano  uhttp://hdl.handle.net/1963/317401152nas a2200121   4500008004300000245007700043210006900120260000900189520075400198100002100952700002100973856003600994       2009                        en_Ud  00aHomogenization of fiber reinforced brittle materials: the extremal cases0 aHomogenization of fiber reinforced brittle materials the extrema  bSIAM3 aWe 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 $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.1 aBarchiesi, Marco1 aDal Maso, Gianni  uhttp://hdl.handle.net/1963/270501010nas a2200145   4500008004300000245005800043210005800101260001300159520057100172100002100743700001900764700002000783700002500803856003600828       2004                        en_Ud  00aHigher order quasiconvexity reduces to quasiconvexity0 aHigher order quasiconvexity reduces to quasiconvexity  bSpringer3 aIn this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems.1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni1 aMorini, Massimiliano  uhttp://hdl.handle.net/1963/2911