TY - RPRT
T1 - Stochastic homogenisation of free-discontinuity problems
Y1 - 2018
A1 - Filippo Cagnetti
A1 - Gianni Dal Maso
A1 - Lucia Scardia
A1 - Caterina Ida Zeppieri
AB - In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas.
UR - http://preprints.sissa.it/handle/1963/35309
U1 - 35617
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -
TY - RPRT
T1 - Gamma-Convergence of Free-discontinuity problems
Y1 - 2017
A1 - Filippo Cagnetti
A1 - Gianni Dal Maso
A1 - Lucia Scardia
A1 - Caterina Ida Zeppieri
AB - We study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper.
PB - SISSA
UR - http://preprints.sissa.it/handle/1963/35276
U1 - 35583
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density
Y1 - 2012
A1 - Maria Giovanna Mora
A1 - Lucia Scardia
AB - The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

PB - Elsevier
UR - http://hdl.handle.net/1963/3466
N1 - 21 pages
U1 - 7112
U2 - Mathematics
U4 - -1
ER -