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 - RPRT
T1 - A bridging mechanism in the homogenisation of brittle composites with soft inclusions
Y1 - 2015
A1 - Marco Barchiesi
A1 - Giuliano Lazzaroni
A1 - Caterina Ida Zeppieri
AB - 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.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/7492
U1 - 7621
ER -
TY - JOUR
T1 - New results on Gamma-limits of integral functionals
Y1 - 2014
A1 - Nadia Ansini
A1 - Gianni Dal Maso
A1 - Caterina Ida Zeppieri
KW - Gamma-convergence
PB - Elsevier
UR - http://hdl.handle.net/1963/5880
U1 - 5745
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -
TY - JOUR
T1 - Gamma-convergence and H-convergence of linear elliptic operators
JF - Journal de Mathématiques Pures et Appliquées, Available online 12 September 2012
Y1 - 2012
A1 - Nadia Ansini
A1 - Gianni Dal Maso
A1 - Caterina Ida Zeppieri
KW - Linear elliptic operators
PB - Elsevier
UR - http://hdl.handle.net/1963/5878
U1 - 5746
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -
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 - Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers
JF - Netw. Heterog. Media 4 (2009) 667-708
Y1 - 2009
A1 - Marco Cicalese
A1 - Antonio DeSimone
A1 - Caterina Ida Zeppieri
AB - In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields.
PB - American Institute of Mathematical Sciences
UR - http://hdl.handle.net/1963/3788
U1 - 538
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -