Gérard Michaille

Learn More
We introduce a simplified model for a multi-material made up of two elastic bodies connected by a strong thin material layer whose stiffness grows as 1 . The model is obtained by identifying the Γ-limit of the stored strain energy functional of the physical problem when the thickness of the intermediate layer tends to zero. The intermediate layer behaves as(More)
In this paper, the main objective is to establish an existence result of a variational model in image segmentation constrained by a given vector field. In the one dimensional case, we give a discrete version converging in a variational way to the continuous model. We finally describe the numerical analysis of this model with application in image(More)
An elementary situation in welding involves the perfect assembly of two adherents and a strong adhesive occupying a thin layer. The bulk energy density of the hyperelastic adherents grows superlinearly while the one of the pseudo-plastic adhesive grows linearly with a stiffness of the order of its thickness ε. We propose a simplified but accurate model by(More)
Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the Γ-limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our(More)
We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order 1 √ ε concentrated on an ε-neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of(More)
— We study the rate of convergence of solutions relative to Dirichlet problems associated with a random quasilinear operator in randomly perforated domains #ƒ R with holes whose size tends to 0. Our direct method allows to extend the results already obtained by an epi-convergence method in the case of symétrie operator with deterministic and constant(More)
We give a new derivation, based on the complementary energy formulation, of a simplified model for a multi-structure made up of two anisotropic hyper-elastic bodies connected by a thin strong material layer. The model is obtained by identifying the Mosco-limit of the stored complementary energy functional when the thickness is of order ε and the stiffness(More)
The main objective of this paper is to introduce and illustrate a new tool stemming from Young measure theory in order to capture concentrations, jump sign and gradient oscillations of sequences of SBV-functions. We show how this notion of measure can be applied for the analysis of approximating solutions of Mumford-Shah type energy functionals in the one(More)