Thesis defense : "Large industrial problems in computational mechanics of contact : performance, reliability and robustness"

by D. Kudawoo et M. Abbas, EDF R&D / AMA

Dzifa Kudawoo defended his PhD the 22th November, 2012 at the Laboratory of Mechanics and Acoustics of Marseille on the subject:

"Large industrial problems in computational mechanics of contact : performance, reliability and robustness"

Summary :
This work concerns the computational mechanics of contact between deformable solids. It is to contribute to improving the performance, reliability and robustness of algorithms and models used in Code_Aster. The goal is to address large-scale industrial problems with computing time efficiency. To achieve this, the formulations and algorithms must take into account the difficulties related to the non-regular mechanics due to Signorini-Coulomb laws and the management of non-linearities due to large deformation and behavior of materials. The first axis of this work is devoted to a better understanding of the formulation called "Lagrangian stabilized" initially implemented in the code. Equivalence between this formulation and the formulation of well-known "augmented Lagrangian" has been demonstrated. The mathematical characteristics related to discrete operators were specified and a total energy formulation was found.

A key issue was to strengthen the weak kinematic condition on the normal contact area via unconstrained optimization techniques. The new formulation is called non-standard augmented Lagrangian". Three new strategies based on the augmented Lagrangian have been implemented. This is the generalized Newton method: it is an optimization method that solves any nonlinearities of the problem in a single loop iteration. Partial Newton’s method is an hybrid method of the previous method in the code called fixed point method and the generalized Newton method. Finally, we introduced a novel way to treat cycling: this phenomenon often occurs during the resolution of the problem and results in the loss of convergence of the algorithms. The new strategy improves the robustness of the algorithms.

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Keywords :
Finite elements, contact-friction, augmented Lagrangian, generalized Newton, cycling, industrial problems, quasi-static, dynamic regularization