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Modélisation de la localisation des déformations dans les milieux adoucissants par une approche eikonale

Abstract : Damage mechanics is commonly used to model the softening behavior of quasi-brittle materials such as concrete. The loss of ellipticity of the equilibrium equations during softening phases can lead to the localization of deformations in areas of infinitesimal size and to spurious energy dissipation. Non-local methods allow to regularize the problem by considering that the behavior of a material point depends on the behavior of material points in its vicinity. In this context, the eikonal non-local method for damage proposes to calculate the non-local interactions according to the evolution of the damage field in order to avoid the pathological damage diffusion observed for the classical integral non-local method where interactions remain constant.The numerical implementation and the study of the regularization properties of the eikonale non-local method is presented in this work. The study is first conducted in a one-dimensional context in order to highlight the influence of damage on the deformation localization process. A loss of objectivity of results with respect to spatial discretization is observed for high damage levels. The transition from the eikonal non-local damage model to a strong discontinuity model is then proposed in order to recover objectivity. The study is then continued in a two-dimensional context using the finite element solver Cast3M and the procedure for calculating non-local interactions in two dimensions is presented. The transition from the eikonal non-local damage model to a strong discontinuity model is developed in the embedded finite element framework. Finally, a procedure for identifying the parameters of the eikonal non-local damage model is proposed. A Gaussian Process Regression model is constructed from the results of numerical simulations of the damage model. The parameters of the damage model are then identified using a genetic optimization algorithm using the Gaussian Process Regression model to estimate the response of the damage model.
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Flavien Thierry. Modélisation de la localisation des déformations dans les milieux adoucissants par une approche eikonale. Génie civil. Université Paris-Saclay, 2021. Français. ⟨NNT : 2021UPAST114⟩. ⟨tel-03509295⟩

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