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International audience; Finite-Element Digital Image Correlation (FE-DIC) now appears highly relevant in the experimental mechanics community thanks to its direct bridge with simulation. However, using the fine FE mesh generated for accurate simulation inevitably requires the proper regularization of the inverse DIC problem. Here, Truncated Hierarchical B-Splines (THBS) are considered in a Free-Form-Deformation DIC approach to regularize FE-DIC in a strong, non-invasive, and adaptive manner. The idea is to embed the fine FE mesh in a THBS box whose unstructured refinement is automatically performed during the process to arrive at an optimal number of Degrees Of Freedom (DOF) for the solution. The FE DOF are related to the THBS DOF so that we end up with a regularized but conventional FE measured field which can be computed from a standard FE-DIC code. The method is also extended to cover stereo-DIC applications.

International audience; Background: Even though the simulations used to describe the failure of laminates are becoming more and more predictive, complex testing under multiaxial loadings is still required to validate the design of structural parts in a wide range of industrial domains. It is thus essential to assess the actual boundary conditions to allow for an objective comparison between testing and calculations, in particular since the structural tests are complex and often leads to buckling. Therefore, accurate estimation of force and moment fluxes applied to the specimen is critical. In this context, stereo DIC has proven to be an important measurement tool and provides very well resolved surface displacement fields, but the exploitation of such measurements to calculate fluxes remains problematic when testing composites. Objectives: The first objective of this study is both to reduce the uncertainty associated with fluxes determination on a complex test and to simplify the extraction process with respect to existing procedures. The second objective is to make this methodology robust to geometrically nonlinear deformations. Methods: In this paper, we propose a new methodology that extracts minimal boundary conditions in the form of 3D mechanically admissible displacements fields. The approach developed uses a Finite-Element Stereo Digital Image Correlation (FE-SDIC) method regularized by the means of mechanical behavior admissibility equations. Results: Results show that the new methodology outputs much more accurate fluxes than classical data generated from multiple differentiations of the displacement fields. Excellent noise robustness is obtained and quantified. Conclusions: Numerical predictions have been satisfactorily compared with experimental data from one structural scale composite specimen under complex testing.

International audience

International audience

A novel approach which combines isogeometric collocation and an equilibriumbased stress recovery technique is applied to analyze laminated composite plates. Isogeometric collocation is an appealing strong form alternative to standard Galerkin approaches, able to achieve high order convergence rates coupled with a significantly reduced computational cost. Laminated composite plates are herein conveniently modeled considering only one element through the thickness with homogenized material properties. This guarantees accurate results in terms of displacements and in-plane stress components. To recover an accurate out-of-plane stress state, equilibrium is imposed in strong form as a post-processing correction step, which requires the shape functions to be highly continuous. This continuity demand is fully granted A novel approach which combines isogeometric collocation and an equilibriumbased stress recovery technique is applied to analyze laminated composite plates. Isogeometric collocation is an appealing strong form alternative to standard Galerkin approaches, able to achieve high order convergence rates coupled with a significantly reduced computational cost. Laminated composite plates are herein conveniently modeled considering only one element through the thickness with homogenized material properties. This guarantees accurate results in terms of displacements and in-plane stress components. To recover an accurate out-of-plane stress state, equilibrium is imposed in strong form as a post-processing correction step, which requires the shape functions to be highly continuous. This continuity demand is fully granted.

International audience

International audience; no abstract

This thesis is dedicated to measurement of 3D shapes, 3D kinematic fields on surfaces and identification of mechanical properties from digital image correlation measurements. This optical method uses cameras as measurement tools. For this reason, a study of the classical camera models used is performed and the description of the digitalization of an image from a continuous to a discrete formalism using the pixel is described. A specific work is dedicated to optical distortions and a method based on digital image correlation to evaluate these distortions is developped.A new method for 3D shapes and 3D displacement fields on surfaces using stereo-correlation is introduced. A numerical description of the observed object is used as a support to perform the correlation. This method lead to a global approach to stereo-correlation. It can be rewrite in a generic case or in particular to be applied to NURBS (Non-Uniform Rational B-Splines) surfaces. The displacement fields is therefore expressed in a NURBS formalism which is completely consistent with the geometrical model used to described the observed shape. Measurements are validated using prescribed motions on a Bezier patch. The feasibility of such a technique in several industrial cases is then studied with for example the measurement of the displacement of a composite part of a landing gear under mechanical loading.Finally, from this isogeometric formulation of full-field measurement, a study of the identification of elastic properties is performed. Two methods inspired from existing approaches are proposed, using full-field measurement and numerical simulations in a common isogeometric formalism to identify parameters of an isotropic linear elastic constitutive law on a both a numerical test case and a uniaxial tensile test., Ces travaux de thèse sont dédiés à la mesure de formes 3D, de champs cinématiques 3D surfaciques et à l'identification de paramètres mécaniques à partir de mesures par corrélation d'images. Cette méthode optique se base sur l'utilisation de caméras comme support de la mesure. Pour cette raison, une étude des différents modèles de caméra classiquement utilisés est effectuée, puis le passage d'un formalisme continu pour la description des images à une approche discrète utilisant la notion de pixel est décrit. Une attention particulière est portée aux distorsions optiques et une approche utilisant la corrélation d'images pour les évaluer est développée. Une nouvelle méthode de mesure de forme 3D et de champs de déplacements 3D surfaciques par stéréo-corrélation d'images est introduite. Elle utilise un modèle numérique de l'objet observé comme support pour la corrélation. Cette méthode mène à une formulation globale de la stéréo-corrélation. Elle peut être écrite dans le cas général et particularisée à des surfaces NURBS (non-uniform rational B-splines). Le champ de déplacement est également exprimé dans un formalisme NURBS complètement cohérent avec le modèle géométrique utilisé pour définir la forme observée. Des mesures sont validées en utilisant des mouvements imposés à un carreau de Bézier usiné. La faisabilité de la technique dans plusieurs cas industriels est également étudiée avec, par exemple, la mesure des déplacements d'une pièce composite de train d'atterrissage chargée mécaniquement. Enfin, à partir de cette formulation isogéométrique de la mesure de champs, une étude de la caractérisation de propriétés élastiques est effectuée. Deux méthodes inspirées d'approches existantes sont ainsi proposées, utilisant des mesures de champs et des calculs numériques dans un formalisme isogéométrique pour identifier des paramètres de loi de comportement élastique isotrope sur un cas test numérique et pour un essai de traction uniaxiale.

A novel approach which combines isogeometric collocation and an equilibriumbased stress recovery technique is applied to analyze laminated composite plates. Isogeometric collocation is an appealing strong form alternative to standard Galerkin approaches, able to achieve high order convergence rates coupled with a significantly reduced computational cost. Laminated composite plates are herein conveniently modeled considering only one element through the thickness with homogenized material properties. This guarantees accurate results in terms of displacements and in-plane stress components. To recover an accurate out-of-plane stress state, equilibrium is imposed in strong form as a post-processing correction step, which requires the shape functions to be highly continuous. This continuity demand is fully granted A novel approach which combines isogeometric collocation and an equilibriumbased stress recovery technique is applied to analyze laminated composite plates. Isogeometric collocation is an appealing strong form alternative to standard Galerkin approaches, able to achieve high order convergence rates coupled with a significantly reduced computational cost. Laminated composite plates are herein conveniently modeled considering only one element through the thickness with homogenized material properties. This guarantees accurate results in terms of displacements and in-plane stress components. To recover an accurate out-of-plane stress state, equilibrium is imposed in strong form as a post-processing correction step, which requires the shape functions to be highly continuous. This continuity demand is fully granted.