TY - JOUR
T1 - Homogenization of fiber reinforced brittle material: the intermediate case
JF - Adv. Calc. Var. 3 (2010) 345-370
Y1 - 2010
A1 - Gianni Dal Maso
A1 - Caterina Ida Zeppieri
AB - We 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.
PB - Walter de Gruyter
UR - http://hdl.handle.net/1963/3607
U1 - 694
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - A higher order model for image restoration: the one dimensional case
JF - SIAM J. Math. Anal. 40 (2009) 2351-2391
Y1 - 2009
A1 - Gianni Dal Maso
A1 - Irene Fonseca
A1 - Giovanni Leoni
A1 - Massimiliano Morini
AB - The 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.
UR - http://hdl.handle.net/1963/3174
U1 - 1127
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Homogenization of fiber reinforced brittle materials: the extremal cases
JF - SIAM J. Math. Anal. 41 (2009) 1874-1889
Y1 - 2009
A1 - Marco Barchiesi
A1 - Gianni Dal Maso
AB - 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 $\\\\varepsilon$ 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.
PB - SIAM
UR - http://hdl.handle.net/1963/2705
U1 - 1396
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Higher order quasiconvexity reduces to quasiconvexity
JF - Arch. Ration. Mech. Anal. 171 (2004) 55-81
Y1 - 2004
A1 - Gianni Dal Maso
A1 - Irene Fonseca
A1 - Giovanni Leoni
A1 - Massimiliano Morini
AB - In 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.
PB - Springer
UR - http://hdl.handle.net/1963/2911
U1 - 1789
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -