My interest fields in Mechanics

• Boundary conditions for capillary fluids (theoritical and numerical study). We investigate the relationship between boundary condition for diffuse iinterfaces and the classical boundary condition for sharp interfaces given by Young's law for contact angle.
• Rayleigh Taylor unstability for Cahn-Hilliard fluids. We show that for very thin films lying under a wall, the Rayleigh Taylor unstability is modified by a term taking into account the interactions between the wall and the interface. This effect is exponetially decreasing with the thickness of the film.
• Motion of a contact line on a plane wall when the interface is a diffuse one. We show that a mass transfer must be present in the vicinity of the contact line. This transfer is very small but it enables us to give a correct equation for the shape of the interface up to the contact with the wall. The results are compared with the results obtained by different assumptions classically used to remove the so-called "paradox of the moving contact line". A numerical study is also performed on a super-calculator.
• Contact angle at the junction of an interface and a rough wall (Mathematical study of the possibility of describing hysteresis phenomenon) collaboration with G. Bouchitté.
• Asymptotic model for describing line tension : energy localized at the junction of an interface and a wall. Collaboration with G. Bouchitté and G. Alberti (Pisa, Italy).
• Study of the Tolman formula which links surface tension to the radius of a droplet when this droplet is extremely small. This formula is difficult to interpret and does not fit experimental results, collaboration with F. del Isola (Roma, Italy) and J. Rotoli (Aquila, Italy).
• Rational thermodynamics modelling of capillary zones, collaboration with F. del Isola (Roma, Italy)
• Modelling of continua in which edge forces are present,collaboration with F. del Isola (Roma, Italy)
• Relaxation of energies partially localized on low dimensional structures. Collaboration with G. Buttazzo (Pisa Italy) and G. Bouchitté.
• Modelling of flows of ceramis doughs. Collaboration with P. Suquet. Laboratoire de Mécanique et d'Acoustique de Marseille.
• Homogeneization of an elastic material containing a network of elastic beams. We show that we can obtain a material of a very new kind.
• Homogenization of pantographic_type trusses.Convergence to one-dimensionnal models the energy of which depend on the strain gradient or on its second gradient.
• Determination of the closure of the set of elasticity functionnals. We show that it is made of all lower semi continuous, objective quadratic forms.
• Variationnal study of non-planar elastic rods. collaboration with C. Pideri. We obtain an asymptotic bound for the Korn constant in a tubular neighborhood of a non planar curve as its radius tends to zero. The results are extended in the case of non linear elasticity, owing the the rigidity lemma of James, Friesecke, Muller. The limit model for a non planar elastic beam with large displacements is obtained.
• Closure of Maxwell equations, collaboration with G. Milton (U.S.A.).
• Closure of of the set of equations of dynamics of elastic bodies, collaboration with G. Milton (U.S.A.).
• Porous media, boundary conditions, shock waves, collaboration with A. Madeo and F. Dell Isola (Italy)