Modeling and simulation of the nucleation and propagation of damage in quasi-brittle materials: Contribution of the variational approach

Abstract : This thesis explores the use of damage models to predict the onset and propagation of cracks in a coherent manner. The results are based on the definition of a bulk energy density and a stability principle. Firstly, we study the nucleation of cracks in a notched domain. The limit loading can be decomposed as the product of three stress intensity factors: a scale effect, a geometry induced factor, function of the angle of the notch, and one due to the damage model. The cracks that appear have a characteristic profile whose width is of the order of the internal length. When the latter is small in front of the dimensions of the structure, by separating scales, and using a local minimum principle, we prove that the length of these damage bands follow Griffith's law. This fundamental results extends those based on global minimization but with a sounder physical base. A thorough investigation of the thermal shock problem leads to a better understanding of the nucleation of cracks. Especially the global property of crack periodicity is exhibited. These results are based on the variational approach and the properties would probably be lost for models developed in an other framework. Finally, numerical results based on an alternate minimization algorithm are established. The nucleation phase is controlled by the critical stress whereas the propagation is governed by the toughness. Size effects in two and three dimensions are captured. These numerical simulations are then confronted to experimental results.
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Submitted on : Tuesday, November 12, 2013 - 9:31:48 AM
Last modification on : Wednesday, March 27, 2019 - 4:16:22 PM
Long-term archiving on : Thursday, February 13, 2014 - 12:00:18 PM

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  • HAL Id : pastel-00903360, version 1

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Paul Sicsic. Modeling and simulation of the nucleation and propagation of damage in quasi-brittle materials: Contribution of the variational approach. Mechanics [physics.med-ph]. Ecole Polytechnique X, 2013. English. ⟨pastel-00903360⟩

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