Multi-level A Priori Hyper-Reduction of mechanical models involving internal variables

International audienceThis paper concerns the adaptation of reduced-order models during simulations of series of elastoviscoplastic problems. In continuation with previous works, this paper aimed at extending the A Priori Hyper-Reduction method (APHR method) for nonlinear thermal problems to nonlinear mechanical problems involving internal variables. This method is an a priori approach because full incremental responses of detailed models are not forecasted in order to build reduced-order models. The recent extension of the Hyper-Reduction method to reduction of mechanical models involving internal variables makes possible the reduction of degrees of freedom and the reduction of integration points. A multi-level formulation is introduced to focus on the capability of the method to perform efficient parallel computations to adapt reduced-order models

Hyper-reduction framework for model calibration in plasticity-induced fatigue

International audienceBackground:Many mechanical experiments in plasticity-induced fatigue are prepared by the recourse to finite element simulations. Usual simulation outputs, like local stress estimations or lifetime predictions, are useful to choose boundary conditions and the shape of a specimen. In practice, many other numerical data are also generated by these simulations. But unfortunately, these data are ignored, although they can facilitate the calibration procedure. The focus of this paper is to illustrate a new simulation protocol for finite-element model calibration. By the recourse to hyper-reduction of mechanical models, more data science is involved in the proposed protocol, in order to solve less nonlinear mechanical equations during the calibration of mechanical parameters. Usually, the location of the crack initiation is very sensitive to the heterogeneities in the material. The proposed protocol is versatile enough in order to focus the hyper-reduced predictions where the first crack is initiated during the fatigue test.Methods:In this paper, we restrict our attention to elastoplasticity or elastoviscoplasticity without damage nor crack propagation. We propose to take advantage of the duration of both the experiment design and the experimental protocol, to collect numerical data aiming to reduce the computational complexity of the calibration procedure. Until experimental data are available, we have time to prepare the calibration by substituting numerical data to nonlinear equations. This substitution is performed by the recourse to the hyper-reduction method (Ryckelynck in J Comput Phys 202(1):346–366, 2005, Int J Numer Method Eng 77(1):75–89, 2009). An hyper-reduced order model involves a reduced basis for the displacement approximation, a reduced basis for stress predictions and a reduced integration domain for the setting of reduced governing equations. The reduced integration domain incorporates a zone of interest that covers the location of the crack initiation. This zone of interest is updated according to experimental observations performed during the fatigue test.Results:Bending experiments have been performed to study the influence of a grain boundary on AM1 superalloy oligocyclic fatigue at high temperature. The proposed hyper-reduction framework is shown to be relevant for the modeling of these experiments. To account for the microstructure generated by a real industrial casting process, the specimen has been machined in a turbine blade. The model calibration aims to identify the loading condition applied on the specimen in order to estimate the stress at the point where the first crack is initiated, before the crack propagation. The model parameters are related to the load distribution on the specimen. The calibration speed-up obtained by hyper-reduction is almost 1000, including the update of the reduced integration domain focused on the experimental location of the crack initiation. The related electric-energy saving is 99.9 %

Modélisation algorithmique par réduction de modèle et maîtrise des événements recurrents inhérents aux problèmes d'optimisation

National audienceNous proposons de traiter efficacement, par une méthode de réduction de modèle, une suite de simulations dans le cadre de l'optimisation de structures. Lorsqu'une base est construite pour représenter les évènements significatifs contenus dans l'ensemble des simulations, les évènements récurrents masquent les évènements spécifiques à chaque simulation. Le processus d'adaptation du modèle d'ordre réduit et l'efficacité du processus d'optimisation peuvent s'en trouver affectés. Nous proposerons un nouvel algorithme d'adaptation permettant d'atténuer l'effet de ces évènements récurrents

Z-set/ZeBuLoN : une suite logicielle pour la mécanique des matériaux et le calcul de structures

National audienceLa suite Z-set/ZéBuLoN est un ensemble d'outils dédiés à la mécanique des matériaux et au calcul de structures co-développés par l'Onera, le Centre des Matériaux (Mines ParisTech) et par la société NW Numerics. Elle intègre différents modules tels qu'un solveur éléments finis, une bibliothèque d'intégration de loi matériaux, un optimiseur permettant de déterminer les paramètres matériaux d'une loi à partir de données d'essais. Certains de ces modules sont indépendants et peuvent être utilisés par des codes commerciaux (Abaqus, Ansys, Samcef, . . .) sous la forme de plugins. Des développements récents ont été faits dans les domaines de la mécanique de la rupture et du calcul haute performance et multimodèle

Nouvelle approche pour la modélisation des problèmes multi-échelles en mécanique : la méthode 95/5

We propose a new micro/macro modelling approach for mechanical problems involving microstructure. This approach is an appealing choice for the treatment of problems involving materials with two behaviour lengths of variation, where it is impossible to define and to apply a single low describing the behaviour of both micro and micro scales. We propose a discretization for which the major part of the studied field is modelled exclusively on a macroscopic scale. Only some relatively small zones, called microscopic patterns, are modelled on a microscopic scale. The implementation of the modelling method rests on: an extension of the behaviour principle from the microscopic scale, in order to deduce a numerical behaviour for the macroscopic scale; the method of constrained natural elements CNEM, in order to be able to insert the microscopic patterns in a macroscopic discretization; and a solver introducing domain decomposition and model reduction to accelerate calculation and to take benefit from the parallel calculators. We proved the effectiveness of our approach on some benchmarks with a good estimation of the solution, and a homogeneous error distribution over the microscopic and macroscopic scales even on the edges. That enables us to consider the use of the suggested approach for the simulation of phenomena located on the edge and affecting the response of the mechanical system (friction, cutting process ...).Nous proposons une nouvelle approche de modélisation micro/macro pour les problèmes multi échelles. Cette approche se destine aux matériaux ayant deux longueurs caractéristiques de variation des propriétés : l'une microscopique et l'autre macroscopique. Ce qui signifie qu'il n'est pas possible de définir une relation de comportement macroscopique unique pour l'ensemble du système étudié. Nous proposons une méthode de discrétisation pour laquelle la majeure partie du domaine étudié est modélisée exclusivement à l'échelle macroscopique, seules quelques zones relativement petites, appelées motifs microscopiques, sont modélisées à l'échelle microscopique. La mise en oeuvre de la méthode de modélisation repose sur : un principe d'extension du comportement de l'échelle microscopique afin d'en déduire une relation de comportement numérique à l'échelle macroscopique ; la méthode des éléments naturels contraints CNEM, afin de pouvoir insérer les motifs microscopiques dans une discrétisation macroscopique ; et une méthode de résolution introduisant décomposition de domaine et réduction de modèle pour accélérer le calcul et tirer profit des calculateurs à architecture parallèle. Nous avons prouvé l'efficacité de notre approche sur des exemples académiques avec une bonne estimation de la solution, et une distribution de l'erreur homogène sur tout le domaine aux échelles microscopique et macroscopique même sur les bords

Nouvelle approche pour la modélisation des problèmes multi-échelles en mécanique (la méthode 95/5)

Nous proposons une nouvelle approche de modélisation micro/macro pour les problèmes multi échelles. Cette approche se destine aux matériaux ayant deux longueurs caractéristiques de variation des propriétés : l'une microscopique et l'autre macroscopique. Ce qui signifie qu'il n'est pas possible de définir une relation de comportement macroscopique unique pour l'ensemble du système étudié. Nous proposons une méthode de discrétisation pour laquelle la majeure partie du domaine étudié est modélisée exclusivement à l'échelle macroscopique, seules quelques zones relativement petites, appelées motifs microscopiques, sont modélisées à l'échelle microscopique. La mise en oeuvre de la méthode de modélisation repose sur : un principe d'extension du comportement de l'échelle microscopique afin d'en déduire une relation de comportement numérique à l'échelle macroscopique ; la méthode des éléments naturels contraints CNEM, afin de pouvoir insérer les motifs microscopiques dans une discrétisation macroscopique ; et une méthode de résolution introduisant décomposition de domaine et réduction de modèle pour accélérer le calcul et tirer profit des calculateurs à architecture parallèle. Nous avons prouvé l'efficacité de notre approche sur des exemples académiques avec une bonne estimation de la solution, et une distribution de l'erreur homogène sur tout le domaine aux échelles microscopique et macroscopique même sur les bords.We propose a new micro/macro modelling approach for mechanical problems involving microstructure. This approach is an appealing choice for the treatment of problems involving materials with two behaviour lengths of variation, where it is impossible to define and to apply a single low describing the behaviour of both micro and micro scales. We propose a discretization for which the major part of the studied field is modelled exclusively on a macroscopic scale. Only some relatively small zones, called microscopic patterns, are modelled on a microscopic scale. The implementation of the modelling method rests on: an extension of the behaviour principle from the microscopic scale, in order to deduce a numerical behaviour for the macroscopic scale; the method of constrained natural elements CNEM, in order to be able to insert the microscopic patterns in a macroscopic discretization; and a solver introducing domain decomposition and model reduction to accelerate calculation and to take benefit from the parallel calculators. We proved the effectiveness of our approach on some benchmarks with a good estimation of the solution, and a homogeneous error distribution over the microscopic and macroscopic scales even on the edges. That enables us to consider the use of the suggested approach for the simulation of phenomena located on the edge and affecting the response of the mechanical system (friction, cutting process ...).PARIS-Arts et Métiers (751132303) / SudocSudocFranceF

Investigation of agglomerated ceramic powders suitable for cold spray

International audienceCold gas spraying is a solid-state deposition process developed for metallic powders as feedstock materials. For ceramic materials, such low temperature-high velocity kinetic process is still questionable but could have interesting advantages. In the CERASOL project (ANR-19-CE08-0009), the nature and the architecture of porous ceramic powders involving agglomerated sub-micrometric grains are investigated. To that purpose, three oxide ceramics powders (alumina, zirconia and yttria) have been prepared for cold spray. These powders were analyzed in order to assess their architecture (composition, particle size, porosity, density, crystallite sizes…). Preliminary cold spray experiments were carried out implementing velocities measurements for various stand-off distances and spraying of coupons with line experiments. The characteristics of the deposited layers have been examined by SEM and XRD in order to discuss the role of the powder architecture on the impact behavior of the nanostructured agglomerated particles. The role of the gas stream that affects the kinetic and the trajectory of the particles is also discussed

3D finite element analysis of a two-surface wear model in fretting tests

International audienceThis article aims at developing a computationally efficient framework to simulate the erosion of two contact surfaces in three-dimensional (3D), depending on the body resistance. The framework involves finite element (FE) resolution of a fretting problem, wear computation via a non-local criterion including a wear distribution parameter (WDP), as well as updating of the geometry and automatic remeshing. Its originality is based on the capability to capture the damage on each surface and obtain local and global results for a quantitative and qualitative analysis. Numerical simulations are carried out for two 3D contact specimens with different values of WDP. The results highlight the importance of correctly modelling wear: One-surface wear model is sufficient from a global point of view (wear volume), or whenever the wear resistance for a body is much higher than that of another one, whereas a 3D two-surface wear model is essential to capturing local effects (contact pressure, wear footprint, etc.) related to the difference in wear resistance of the bodies