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Modélisation, analyse et simulation numérique de solides combinant plasticité, rupture et dissipation visqueuse

Abstract : In this work, we are interested in modeling, mathematical analysis and numerical simulation of a class of models that combine several mecanisms of dissipation: plasticity, fracture and viscous dissipation. Firslty, we construct evolution models containing plasticity, viscoplasticity, linear kinematic hardening and fracture. In particular, we show for our models a Clausius-Duhem like thermodynamical inequality. Then, we prove an existence result for evolutions for an elasto-visco-plastic model with regularized fracture using the Ambrosio-Tortorelli functional and for an elasto-viscoplastic model with kinematic hardening and fractures regularized with the modified r-Laplacian Ambrosio-Tortorelli functional. Finally, we study from a numerical point of view our models in function of various mecanical parameters. We also propose an extension of the backtracking algorithm for materials with memory. In the end, we test numerically one of our models on a geophysical Peltzer and Tapponnier's experiment of plasticine that models failure propagation in the Earth crust.
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Lukáš Jakabčin. Modélisation, analyse et simulation numérique de solides combinant plasticité, rupture et dissipation visqueuse. Modélisation et simulation. Université de Grenoble, 2014. Français. ⟨NNT : 2014GRENM043⟩. ⟨tel-01549112⟩

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