Gérard Michaille

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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)
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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)
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)
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)
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)
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