19 citations · 58 across the 25 of their papers we have counts for
31 papers
Critical points of the two-dimensional Ambrosio-Tortorelli functional with convergence of the phase-field energy
Jean-François Babadjian, Martin Rakovsky, Rémy Rodiac
We consider a family of critical points of the Ambrosio-Tortorelli functional. Assuming a uniform energy bound, the sequence $\…
Curvature penalization of strongly anisotropic interfaces models and their phase-field approximation
Jean-François Babadjian, Blanche Buet, Michael Goldman
This paper studies the effect of anisotropy on sharp or diffuse interfaces models. When the surface tension is a convex function of the normal to the interface, the anisotropy is s…
Uniqueness, regularity and characteristic flow for a non strictly convex singular variational problem
Jean-Francois Babadjian, Gilles Francfort
This work addresses the question of uniqueness and regularity of the minimizers of a convex but not strictly convex integral functional with linear growth in a two-dimensional sett…
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…
On the Convergence of critical points of the Ambrosio-Tortorelli functional
Jean-François Babadjian, Vincent Millot, Rémy Rodiac
This work is devoted to study the asymptotic behavior of critical points of the Ambrosio-Tortorelli functional. Under a uniform…
Mixed boundary conditions as limits of dissipative boundary conditions in dynamic perfect plasticity
Jean-François Babadjian, Randy Llerena
This paper addresses the well posedness of a dynamical model of perfect plasticity with mixed boundary conditions for general closed and convex elasticity sets. The proof relies on…
Discrete approximation of the Griffith functional by adaptive finite elements
Jean-François Babadjian, Élise Bonhomme
This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem i…
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…
Continuity equation and characteristic flow for scalar Hencky plasticity
Jean-Francois Babadjian, Gilles A. Francfort
We investigate uniqueness issues for a continuity equation arising out of the simplest model for plasticity, Hencky plasticity. The associated system is of the form $\rm{ curl\;}(μ…
Dissipative boundary conditions and entropic solutions in dynamical perfect plasticity
Jean-François Babadjian, Vito Crismale
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studi…
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…
Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion
Maria Giovanna Mora, Jean-François Babadjian
This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic - perfectly plastic materials obeying a Drucker-Pra…
Hyperbolic structure for a simplified model of dynamical perfect plasticity
Jean-Francois Babadjian, Clément Mifsud
This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' syst…
A note on the derivation of rigid-plastic models
Jean-François Babadjian, Gilles A. Francfort
This note is devoted to a rigorous derivation of rigid-plasticity as the limit of elasto-plasticity when the elasticity tends to infinity.
Reduced models for linearly elastic thin films allowing for fracture, debonding or delamination
Jean-Francois Babadjian, Duvan Henao
This work is devoted so show the appearance of different cracking modes in linearly elastic thin film systems by means of an asymptotic analysis as the thickness tends to zero. By…
Relaxation approximation of Friedrich's systems under convex constraints
Jean-François Babadjian, Clément Mifsud, Nicolas Seguin
This paper is devoted to present an approximation of a Cauchy problem for Friedrichs' systems under convex constraints. It is proved the strong convergence in L^2\_{loc} of a parab…
Energy release rate for non smooth cracks in planar elasticity
Jean-François Babadjian, Antonin Chambolle, Antoine Lemenant
This paper is devoted to the characterization of the energy release rate of a crack which is merely closed, connected, and with density at the tip. First, the blow-up limit o…
Traces of functions of bounded deformation
Jean-François Babadjian
This paper is devoted to give a simplified proof of the trace theorem for functions of bounded deformation defined on bounded Lipschitz domains of . As a consequence,…
Unilateral gradient flow of the Ambrosio-Tortorelli functional by minimizing movements
Jean-Francois Babadjian, Vincent Millot
Motivated by models of fracture mechanics, this paper is devoted to the analysis of unilateral gradient flows of the Ambrosio-Tortorelli functional, where unilaterality comes from…
Homogenization of variational problems in manifold valued BV-spaces
Jean-Francois Babadjian, Vincent Millot
This paper extends the result of \cite{BM} on the homogenization of integral functionals with linear growth defined for Sobolev maps taking values in a given manifold. Through a $Γ…
Homogenization of variational problems in manifold valued Sobolev spaces
Jean-Francois Babadjian, Vincent Millot
Homogenization of integral functionals is studied under the constraint that admissible maps have to take their values into a given smooth manifold. The notion of tangential homogen…
Dimensional reduction for energies with linear growth involving the bending moment
Jean-Francois Babadjian, Elvira Zappale, Hamdi Zorgati
A -convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model w…
A variational approach to the local character of G-closure: the convex case
Jean-Francois Babadjian, Marco Barchiesi
This article is devoted to characterize all possible effective behaviors of composite materials by means of periodic homogenization. This is known as a -closure problem. Under c…