Publications

       -->This work concerns the asymptotic analysis of the spatially discretized brittle damage model of Francfort and Marigo, based on the Γ-convergence of the total energies (which are restricted to continuous and piecewise affine vectorial displacements), within different regimes where the damaged regions concentrate on vanishingly small sets while the stiffness of the damaged material degenerates to 0. In this setting, the mesh size, the localization of damage, and the stiffness loss inside damaged regions all compete simultaneously in non-trivial ways according to the scaling law under consideration. The spatial discretization of the model turns out to be a crucial feature of the analysis, as the mesh size induces a minimal scale of spatial oscillations for admissible displacements. I show that fracture-like behavior only appears asymptotically when the mesh size and the concentration of damage are of the same order. This result answers a question raised by previous works, which showed the absence of fracture in the asymptotic analysis of the spatially continuous Francfort and Marigo model, regardless of the scaling law governing the interaction between damage localization and stiffness loss.   


       --> We prove the homogenization of the so-called "double porosity" model in a random setting, when the resonant inclusions are neither uniformly bounded nor separated. This mesoscopic model, used to describe flows in fractured porous media, arises as the limit of a diffusion process in a highly heterogeneous material composed of two pure phases: a connected "intact" phase (with conductivity of order one), randomly perforated by a dense network of small inclusions belonging to a second, nearly "soft" phase, whose conductivity scales like the square of their size and tends to zero. In this specific regime, so-called resonance phenomena occur, in the sense that the homogenized model retains memory of the nontrivial interactions between the micro- and macroscopic scales of the material.

       --> This work questions the interpretation of the plastic behavior (permanent deformation) of a material as the limiting result of a brittle damage process. While previous studies have provided a positive answer in the static case (i.e., without time evolution), it is natural to investigate whether this connection still holds when the material evolves slowly under varying loads (but without inertia effects: quasi-static evolution). In one dimension, I show that this correspondence does not always hold: depending on the boundary conditions imposed on the material, the limiting behavior may fail to correspond to a perfect plasticity model.

       --> We prove that the isotropic two-dimensional Griffith energy (introduced in fracture mechanics) can be approximated, in the sense of Γ-convergence, by a sequence of discrete brittle damage energies (i.e., integral functionals restricted to continuous, piecewise affine displacements). The mesh is treated as a variable of the problem, providing enough flexibility to recover an isotropic surface energy (i.e., independent of the fracture orientation) in the limit.

  • Here, you can find the manuscript of my thesis.

Past events

  • I co-organized the Analysis and PDE seminar of ULB for one year in 2025.
  • Between 2021 and 2023, I co-organized the work group of calculus of variations GT CalVa, between the Universities of Paris-Saclay, Paris-Diderot, and Paris-Dauphine.
  • Co-organization of the Journée de rentrée 2023 du GT CalVa at Université Paris-Cité, for a day of talks on different topics in Calculus of Variations.
  • Co-organization of the event Journée de fin d'année 2022 du GT CalVa at the LMO, for a day of talks on some topics in Calculus of Variations.

Invited talks