Soutenance de thèse de Rémi Haustrate

The development of full-field measurement techniques in experimental mechanics has provided a large amount of data that can be used to analyze the mechanical behavior and calibrate model parameters. Heterogeneous identification, which aims to determine fields of properties, benefits greatly from these spatially dense measurements. Representing a field requires a large number of parameters, which creates additional challenges. First, an increase in the computational cost of the methods and second an increase in the impact of measurement uncertainties on the identification result.

To address these challenges, an approach based on the equilibrium gap method, which has a low computational cost, is proposed. Using a covariance-weighted norm reduces the effect of uncertainties and makes explicit the link with the Finite Element Method Updating approach. The use of a reduced basis to represent heterogeneous material parameters is proposed to control the effects of uncertainties on the solution. The size of the basis is related to that of the heterogeneities it can represent. Heuristics are proposed to find the optimal size of the reduced basis, which is the best compromise between interpolation errors (predominant with a small reduced basis) and errors due to uncertainties (predominant with a large reduced basis).  The proposed approach is ultimately applied to a complete experiment containing a sequence of measured displacement fields. A reduced spatio-temporal basis is used to represent the heterogeneous parameters that vary over time.

 

Composition du Jury :

• Pierre FEISSEL : Professeur des universités - Université de Technologie de Compiègne, Laboratoire Roberval, Rapporteur
• Pierre KERFRIDEN : Professeur des Universités - Mines Paris, Centre des Matériaux, Rapporteur
• Michel GRÉDIAC : Professeur des universités - Université de Clermont, Institut Pascal, Examinateur
• Guillaume PUEL : Professeur des universités - Université Paris-Saclay, Laboratoire de Mécanique Paris-Saclay, Examinateur
• Jean-Noël PÉRIÉ : Professeur des universités - Université Fédérale Toulouse Midi-Pyrénées, Institut Clément Ader, Examinateur
• Sinan ACIKGOZ : Associate Professor - University of Oxford, Departement of Engineering Science, Examinateur