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Section: New Results

Composites Materials

  • Participants: Giulia Bellezza, Mathieu Colin and Mario Ricchiuto

  • Corresponding member: Mario Ricchuito

    Self-healing is an important phenomenon in new-generation refractory ceramic-matrix composites, obtained by the oxidation of a glass-forming phase in the composite. The dynamics of oxygen diffusion, glass formation and flow are the basic ingredients of a self-healing model that has been developed here in 2D in a trans-verse crack of a mini composite [11]. The presented model can work on a realistic image of the material section and is able to simulate healing and quantify the exposure of the material to oxygen, a prerequisite for its lifetime prediction. Crack reopening events are handled satisfactorily, and secondary healing can be simulated. This papers describes and discusses a typical case in order to show the model potentialities.

    Additional work involve two main topics. The first one is dedicated to the modeling of the propagation of a self-healing oxyde in a crack. The aim here is to introduce new models which describe both the self-healing behavior and oxygen diffusion towards fibers. In general, the evolution of an incompressible fluid can be described by the Navier-Stokes equations. However, we observe that a direct numerical method applied to these equations will induce a significant computational cost, especially in our case, due to the long lifespan of the material. Thus, alternatively, we derive several asymptotic models obtained by performing a dimensional analysis on the Navier-Stokes equations : we focus here on shallow water models and thin film models. The second aspect under study is more theoretical. We propose in the full generality a link between the BD entropy introduced by D. Bresch and B. Desjardins for the viscous shallow-water equations and the Bernis-Friedman (called BF) dissipative entropy introduced to study the lubrications equations. Different dissipative entropies are obtained playing with the drag terms on the viscous shallow water equations. It helps for instance to prove global existence of nonnegative weak solutions for the lubrication equations starting from the global existence of nonnegative weak solutions for appropriate viscous shallow-water equations.