46 citations · 82 across the 9 of their papers we have counts for
11 papers
Velocity optimization of self-equilibrated obstacles in a two-dimensional viscous flow
Gilles A. Francfort, Alessandro Giacomini, Scott Weady
An obstacle is immersed in an externally driven 2D Stokes or Navier-Stokes fluid. We study the self-equilibration conditions for that obstacle under steady state assumptions on the…
Liquid Filled Elastomers: From Linearization to Elastic Enhancement
Juan Casado Dìaz, Gilles A. Francfort, Oscar Lopez-Pamies +1
Surface tension at cavity walls can play havoc with the mechanical properties of perforated soft solids when the cavities are filled with a fluid. This study is an investigation of…
Enhancement of elasto-dielectrics by homogenization of active charges
Gilles A. Francfort, Antoine Gloria, Oscar Lopez-Pamies
We investigate the PDE system resulting from even electromechanical coupling in elastomers. Assuming a periodic microstructure and a periodic distribution of micro-charges of a pre…
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…
A two-dimensional labile aether through homogenization
Marc Briane, Gilles A. Francfort
Homogenization in linear elliptic problems usually assumes coercivity of the accompanying Dirichlet form. In linear elasticity, coercivity is not ensured through mere (strong) elli…
Approximation of a Brittle Fracture Energy with a Constraint of Non-Interpenetration
Antonin Chambolle, Sergio Conti, Gilles Francfort
Linear fracture mechanics (or at least the initiation part of that theory) can be framed in a variational context as a minimization problem over a SBD type space. The corresponding…
Isotropy prohibits the loss of strong ellipticity through homogenization in linear elasticity
Gilles Francfort, Antoine Gloria
Since the seminal contribution of Geymonat, M{ü}ller, and Triantafyllidis, it is known that strong ellipticity is not necessarily conserved by homogenization in linear elasticity.…
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.
Spatial heterogeneity in 3D-2D dimensional reduction
Jean-Francois Babadjian, Gilles A. Francfort
A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le…
Quasi-static evolution in brittle fracture: the case of bounded solutions
Gianni Dal Maso, Gilles A. Francfort, Rodica Toader
The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex…
Quasistatic crack growth in finite elasticity
Gianni Dal Maso, Gilles A. Francfort, Rodica Toader
In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of -dimensional finite elastic…