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On some multi-phase problems in continuum mechanics

Abstract : This work discusses a series of modelling problems in continuum mechanics. The first part is devoted to the mathematical analysis of some diffuse interface models in phase separation of binary mixtures (e.g., coarsening of alloys or bistable polymeric fluids). The second part discusses the function of electronic devices (in particular p-n junctions) under mechanical deformations. The third part presents a model for lifetime predictions in polycrystalline metals under periodic loading. A typical phase separation model is the well-known model H, constructed by coupling the convective Cahn-Hilliard equation with the Navier-Stokes system through the so-called Korteweg force. Here we consider some variants of the model which account, e.g., for shear dependent viscosity or chemically reacting components. We first study basic issues like existence, uniqueness and regularity of solutions. Then we analyze the long-time behaviour of the infinite dimensional dissipative dynamical systems generated by the systems studied. More precisely, we prove the existence of global attractors, exponential attractors, pullback attractors and trajectories attractors for the corresponding dynamical systems. Also, we discuss the robustness of such invariant sets with respect to perturbations of some parameters of the model. The results obtained represent natural extensions of the properties known for single fluid flows, whose features are considered a benchmark for all new techniques proposed in the literature. Finally, as a more realistic description of phase separation phenomena, we introduce a Cahn-Hilliard equation accounting for nonlocal interactions through a singular kernel. In this case some well-posedness and regularity results are demonstrated. The second part of this work is devoted to the study of the coupling effects between mechanical and electronic properties in semiconductors. The modelling of the electronic device is based on the drift-diffusion model for electrons and holes. The device is viewed as a standard macroscopic continuum and the objective is to understand the effects of mechanical strain on the electronic properties of the semiconductor and in particular its effects on the characteristic curve of a p-n junction. This permits to propose a variational formulation of the classical drift-diffusion system and to derive a thermodynamically consistent model for the coupled electromechanical phenomena. The strain mainly influences the mobility coefficients and the generation/recombination term. Two approximate solutions are discussed, one based on only physical assumptions and one involving asymptotic expansions. This part of the work is a preliminary step towards the understanding of the properties of flexible electronic devices. The final part of the thesis presents an application of the theory of dynamical systems to predict the lifetime of polycrystalline metals undergoing a high cycle fatigue regime. A new model is proposed and compared with the existing literature.
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Contributor : Stefano Bosia <>
Submitted on : Friday, January 3, 2014 - 7:35:48 PM
Last modification on : Wednesday, October 14, 2020 - 3:52:13 AM
Long-term archiving on: : Thursday, April 3, 2014 - 10:40:25 PM


  • HAL Id : pastel-00923691, version 1


Stefano Bosia. On some multi-phase problems in continuum mechanics. Mechanics of materials [physics.class-ph]. Ecole Polytechnique X, 2013. English. ⟨pastel-00923691⟩



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