@article {2018,
	title = {Stochastic homogenisation of free-discontinuity problems},
	number = {SISSA;05/2018/MATE},
	year = {2018},
	abstract = {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.},
	url = {http://preprints.sissa.it/handle/1963/35309},
	author = {Filippo Cagnetti and Gianni Dal Maso and Lucia Scardia and Caterina Ida Zeppieri}
}
@article {2017,
	title = {Gamma-Convergence of Free-discontinuity problems},
	number = {SISSA;18/2017/MATE},
	year = {2017},
	institution = {SISSA},
	abstract = {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.},
	url = {http://preprints.sissa.it/handle/1963/35276},
	author = {Filippo Cagnetti and Gianni Dal Maso and Lucia Scardia and Caterina Ida Zeppieri}
}
@article {2015,
	title = {A bridging mechanism in the homogenisation of brittle composites with soft inclusions},
	number = {SISSA;02/2015/MATE},
	year = {2015},
	institution = {SISSA},
	abstract = {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.},
	url = {http://urania.sissa.it/xmlui/handle/1963/7492},
	author = {Marco Barchiesi and Giuliano Lazzaroni and Caterina Ida Zeppieri}
}
@article {2012,
	title = {New results on Gamma-limits of integral functionals},
	number = {Annales de l{\textquoteright}Institut Henri Poincare. Analyse Non Lineaire},
	year = {2014},
	publisher = {Elsevier},
	keywords = {Gamma-convergence},
	doi = {10.1016/j.anihpc.2013.02.005},
	url = {http://hdl.handle.net/1963/5880},
	author = {Nadia Ansini and Gianni Dal Maso and Caterina Ida Zeppieri}
}
@article {2012,
	title = {Gamma-convergence and H-convergence of linear elliptic operators},
	journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es, Available online 12 September 2012},
	number = {SISSA;04/2012/M},
	year = {2012},
	publisher = {Elsevier},
	keywords = {Linear elliptic operators},
	doi = {10.1016/j.matpur.2012.09.004},
	url = {http://hdl.handle.net/1963/5878},
	author = {Nadia Ansini and Gianni Dal Maso and Caterina Ida Zeppieri}
}
@article {2010,
	title = {Homogenization of fiber reinforced brittle material: the intermediate case},
	journal = {Adv. Calc. Var. 3 (2010) 345-370},
	number = {SISSA;14/2009/M},
	year = {2010},
	publisher = {Walter de Gruyter},
	abstract = {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.},
	doi = {10.1515/ACV.2010.011},
	url = {http://hdl.handle.net/1963/3607},
	author = {Gianni Dal Maso and Caterina Ida Zeppieri}
}
@article {2009,
	title = {Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers},
	journal = {Netw. Heterog. Media 4 (2009) 667-708},
	year = {2009},
	publisher = {American Institute of Mathematical Sciences},
	abstract = {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.},
	doi = {10.3934/nhm.2009.4.667},
	url = {http://hdl.handle.net/1963/3788},
	author = {Marco Cicalese and Antonio DeSimone and Caterina Ida Zeppieri}
}
