Simulation numérique d'impact en dynamique rapide de matériaux hyper-élastiques par la méthode X-FEM

National audienceLa simulation numérique en dynamique rapide de structures composées de matériaux hyper-élastiques peut s’avérer fastidieuse surtout si l’on souhaite obtenir une bonne qualité de résultats. La distorsion excessive des éléments finis du maillage au cours du temps, qui conduit à une dégradation du pas de temps critique, impose par exemple l’utilisation de techniques de type ALE. Nous proposons dans cet article une méthode alternative consistant à utiliser un maillage régulier unique via la méthode X-FEM et dont le principal atout est de simplifier les procédures de remaillage

Modélisation et simulation numérique de l'emboutissage d'un renfort tissé sec : Sensibilité de l'angle de cisaillement aux paramètres du procédé

Le présent travail a pour objectif de présenter une étude de sensibilité des modèles numériques réalisés avec le code ABAQUS, vis-à-vis de la variation des paramètres du procédé d'emboutissage, ainsi que l'effet d'orientation initiale du renfort, le type (coque ou membrane) et la taille du maillage. La simulation de la mise en forme est réalisée à l'échelle macroscopique en considérant le renfort comme un milieu continu. Cette approche continue s'appuie sur une loi de comportement hypoélastique qui a l'aptitude de suivre la rotation des fibres (directions d'anisotropie) au cours de la mise en forme. Cette loi de comportement est implémentée dans le code de calcul des éléments finis ABAQUS /explicit en utilisant une subroutine VUMAT

A neural network-based data-driven local modeling of spotwelded plates under impact

Solving large structural problems with multiple complex localized behaviors is extremely challenging. To address this difficulty, both intrusive and non-intrusive Domain Decomposition Methods (DDM) have been developed in the past, where the refined model (local) is solved separately in its own space and time scales. In this work, the Finite Element Method (FEM) at the local scale is replaced with a data-driven Reduced Order Model (ROM) to further decrease computational time. The reduced model aims to create a low-cost, accurate and efficient mapping from interface velocities to interface forces and enable the prediction of their time evolution. The present work proposes a modeling technique based on the Physics-Guided Architecture of Neural Networks (PGANNs), which incorporates physical variables other than input/output variables into the neural network architecture. We develop this approach on a 2D plate with a hole as well as a 3D case with spot-welded plates undergoing fast deformation, representing nonlinear elastoplasticity problems. Neural networks are trained using simulation data generated by explicit dynamic FEM solvers. The PGANN results are in good agreement with the FEM solutions for both test cases, including those in the training dataset as well as the unseen dataset, given the loading type is present in the training set

Eléments mixtes de contact frottant en grandes transformations et applications

CHATENAY MALABRY-Ecole centrale (920192301) / SudocSudocFranceF

Multipatch isogeometric mortar methods for thick shells

International audienceThis paper introduces, analyzes and validates isogeometric mortar methods for the solution of thick shells problems which are set on a multipatch geometry. A particular attention will be devoted to the introduction of a proper formulation of the coupling conditions, with a particular interest on augmented lagrangian formulations, to the choice and validation of mortar spaces, and to the derivation of adequate integration rules. The relevance of the proposed approach is assessed numerically on various significative examples

Analyse isogéométrique : méthodes multipatchs et quadratures gaussiennes optimisées

International audienceLe concept d’analyse isogéométrique (IGA) permet de lier plus directement la conception assistée par ordinateur à l’étape d’analyse par l’utilisation de fonctions B-splines communes, plus riches que les fonctions de Lagrange utilisées en éléments finis. La régularité élevée de ces fonctions ne permet pas de se soustraire aux problèmes de verrouillages si une quadrature Gaussienne complète est envisagée. Ce résumé propose des règles d’intégrations optimisées et validées dans le cas d’un domaine unique. Une extension est proposée dans le cadre de patchs multiples pour différents types de discrétisation spatiale

Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams

International audienceA general mathematical framework is proposed, in this paper, to define new quadrature rules in the context of BB-spline/NURBS-based isogeometric analysis. High order continuity across the elements within a patch turned out to have higher accuracy than C0C0 finite elements, as well as a better time efficiency. Unfortunately, a maximum regularity accentuates the shear and membrane locking in thick structural elements. The improved selective reduced integration schemes are given for uni-dimensional beam problems, with basis functions of order two and three, and can be easily extended to higher orders. The resulting BB-spline/NURBS finite elements are free from membrane and transverse shear locking. Moreover, no zero energy modes are generated. The performance of the approach is evaluated on the classical test of a cantilever beam subjected to a distributed moment, and compared to Lagrange under-integrated finite elements

Formulation d'un élément coque en analyse isogéométrique pour la simulation du choc

International audienceDans cet article, nous proposons, pour l'analyse isogéométrique, un modèle de coque tridimensionnel dégénéré basé sur une cinématique du premier ordre dans l'épaisseur avec prise en compte du cisaillement transversal (théorie de Reissner-Mindlin). Nous examinons diverses approches pour la description de la géométrie et nous les comparons sur des cas tests linéaires et non-linéaires. Le résultats présentés sont comparés à ceux obtenus avec un modèle volumique ainsi qu'aux solutions de référence données dans la bibliographie

Stable time step estimates for NURBS-based explicit dynamics

International audienceAutomobile crashworthiness is a complex application for numerical methods in dynamics of structures which includes many high non-linearities. Explicit techniques are widely used for structural dynamics dealing with difficult and large problems that prevent the use of implicit methods. We propose, in this paper, a deep study of the stable time step, which guarantees the stability of the method, and its estimates, for one-dimensional and two-dimensional problems. Element and nodal time steps are presented and adapted to highly regular B-spline and NURBS functions, in the context of isogeometric analysis. The size of the proposed stable time estimates benefits from the properties of regularity and extended support of the basis. Their performance is assessed and compared in several examples, with an arbitrary mesh, uniform or non-uniform, and considering polynomial orders from one to five. The smoothness and order of the polynomials have a significant effect on the stable time step and its estimates. Several lumping schemes of the mass matrix are presented and their accuracy is assessed

A Reduced Integration for Reissner-Mindlin Non-linear Shell Analysis Using T-Splines

International audienceWe propose a reduced shell element for Reissner-Mindlin geometric non-linear analysis within the context of T-spline analysis. The shell formulation is based on the displacements and a first order kinematic in the thickness is used for the transverse shear strains. A total Lagrangian formulation is considered for the finite transformations. The update of the incremental rotations is made using the quaternion algebra. The standard two-dimensional reduced quadrature rules for structured B-spline and NURBS basis functions are extended to the more flexible T-meshes. The non-uniform Gauss-Legendre and patchwise reduced integrations for quadratic shape functions are both presented and compared to the standard full Gauss-Legendre scheme. The performance of the element is assessed with linear and geometric non-linear two-dimensional problems in structural analysis. The effects of mesh distortion and local refinement, using both full and reduced numerical quadratures, are evaluated