PhD thesis : "Research of bifurcated solutions and study of their stability in damage problems"

Jerome Beaurain defend his PhD thesis on the subject Research of bifurcated solutions and study of their stability in damage problems Wednesday, December 14th at 13:30 at the University Pierre et Marie Curie, building 55 / 65, room 211.

Abstract : This work is concerned with the development and the implementation of a numerical optimization algorithm in a industrial software for studying the stability of non local gradient damage numerical solutions given by finite elements method. Stability is a fundamental concept, that takes into account the existence of multiple solutions which could emerge due to the softening constitutive laws generally used to represent the irreversible damage of materials like concrete. Among all those solutions, only stable ones, invariant by little perturbations, could be physically observed. The difficulty is to take care of the irreversible constraint of damage which drives to define a stability criterion by the positivity of the second derivative of the total energy in the direction of increasing damage. This leads numerically to ensure the positivity of the minimum of a quadratic form, using the second derivative matrix and subjected to inequalities constraints. In conclusion, the aim of the work is to implement in the EDF R&D Code_Aster software an efficient and robust numerical constraints minimization algorithm, adapted to different damage modelling, and to improve it using test cases found in the literature.

Keywords : non local damage, softening constitutive laws, finite elements method, stability, numerical optimization algorithm.

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