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

9 November 2011

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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