29 citations · 57 across the 12 of their papers we have counts for
21 papers
Shape optimization of light structures with general Hooke's laws
Dimitrios Andreakis, Flaviana Iurlano, Filip Rindler
For the minimum-compliance shape optimization problem it was established recently [\textit{Duke Math.\ J.} 172 (2023), 43--103] that a sequence of approximately optimal shapes of e…
Transition from Continuous to Jumping Solutions in 2D Quasi-static Elastic Contact Problems with Coulomb Friction: the Mathematics Underlying the Onset of Brake Squeal
Patrick Ballard, Flaviana Iurlano
We formulate the quasi-static elastic contact problem with Coulomb friction in a very general setting, with possible jumps in time for both the load and the solution. Exploiting id…
Superlinear free-discontinuity models: relaxation and phase-field approximation
Sergio Conti, Matteo Focardi, Flaviana Iurlano
In this paper we develop the Direct Method in the Calculus of Variations for free-discontinuity energies whose bulk and surface densities exhibit superlinear growth, respectively f…
Piecewise rank-one approximation of vector fields with measure derivatives
Jean-Francois Babadjian, Flaviana Iurlano
This work adresses the question of density of piecewise constant (resp. rigid) functions in the space of vector valued functions with bounded variation (resp. deformation) with res…
Approximation of functions with possibly infinite jump set
Sergio Conti, Matteo Focardi, Flaviana Iurlano
We prove an approximation result for functions such that is -integrable, , and is integrable over the jump set…
Convergence of critical points for a phase-field approximation of 1D cohesive fracture energies
Marco Bonacini, Flaviana Iurlano
Variational models for cohesive fracture are based on the idea that the fracture energy is released gradually as the crack opening grows. Recently, [Conti, Focardi, and Iurlano, An…
Existence Results for the Time-incremental Elastic Contact Problem with Coulomb Friction in 2D
Patrick Ballard, Flaviana Iurlano
In this article, the structure of the incremental quasistatic contact problem with Coulomb friction in linear elasticity (Signorini-Coulomb problem) is unraveled and sharp existenc…
Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy
Sergio Conti, Matteo Focardi, Flaviana Iurlano
We consider a family of vectorial models for cohesive fracture, which may incorporate -invariance. The deformation belongs to the space of generalized functions of…
Homogenization of friction in a 2D linearly elastic contact problem
Patrick Ballard, Flaviana Iurlano
Contact problems with Coulomb friction in linear elasticity are notoriously difficult and their mathematical analysis is still largely incomplete. In this paper, a model problem wi…
Shape optimization of light structures and the vanishing mass conjecture
Jean-Francois Babadjian, Flaviana Iurlano, Filip Rindler
This work proves rigorous results about the vanishing-mass limit of the classical problem to find a shape with minimal elastic compliance. Contrary to all previous results in the m…
Cohesive fracture in 1D: quasi-static evolution and derivation from static phase-field models
Marco Bonacini, Sergio Conti, Flaviana Iurlano
In this paper we propose a notion of irreversibility for the evolution of cracks in presence of cohesive forces, which allows for different responses in the loading and unloading p…
Concentration versus oscillation effects in brittle damage
Jean-Francois Babadjian, Flaviana Iurlano, Filip Rindler
This work is concerned with an asymptotic analysis, in the sense of -convergence, of a sequence of variational models of brittle damage in the context of linearized elasticity.…
Partial regularity for the crack set minimizing the two-dimensional Griffith energy
Jean-François Babadjian, Flaviana Iurlano, Antoine Lemenant
In this paper we prove a regularity result for minimizers of the planar Griffith functional arising from a variational model of brittle fracture. We prove that a…
A note on the Hausdorff dimension of the singular set of solutions to elasticity type systems
Sergio Conti, Matteo Focardi, Flaviana Iurlano
We prove partial regularity for minimizers to elasticity type energies in the nonlinear framework {with -growth, ,} in dimension . It is an open problem in such a…
Approximation of functions with small jump sets and existence of strong minimizers of Griffith's energy
Antonin Chambolle, Sergio Conti, Flaviana Iurlano
We prove that special functions of bounded deformation with small jump set are close in energy to functions which are smooth in a slightly smaller domain. This permits to generaliz…
Approximation of fracture energies with -growth via piecewise affine finite elements
Sergio Conti, Matteo Focardi, Flaviana Iurlano
The modeling of fracture problems within geometrically linear elasticity is often based on the space of generalized functions of bounded deformation , ,…
Existence of strong minimizers for the Griffith static fracture model in dimension two
Sergio Conti, Matteo Focardi, Flaviana Iurlano
We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields…
Existence of minimizers for the d stationary Griffith fracture model
Sergio Conti, Matteo Focardi, Flaviana Iurlano
We consider the variational formulation of the Griffith fracture model in two spatial dimensions and prove existence of strong minimizers, that is deformation fields which are cont…
Integral representation for functionals defined on in dimension two
Sergio Conti, Matteo Focardi, Flaviana Iurlano
We prove an integral representation result for functionals with growth conditions which give coercivity on the space , for . The space of fu…
Which special functions of bounded deformation have bounded variation?
Sergio Conti, Matteo Focardi, Flaviana Iurlano
Functions of bounded deformation () arise naturally in the study of fracture and damage in a geometrically linear context. They are related to functions of bounded variation ($…
Phase field approximation of cohesive fracture models
Sergio Conti, Matteo Focardi, Flaviana Iurlano
We obtain a cohesive fracture model as a -limit of scalar damage models in which the elastic coefficient is computed from the damage variable through a function of the…