Study of some optimal XFEM type methods

The XFEM method in fracture mechanics is revisited. A first improvement is considered using an enlarged fixed enrichment subdomain aroud the crack tip and a bonding condition for the corresponding degree of freedom. An efficient numerical integration rule is introduced for the nonsmooth enrichment functions. The lack of accuracy due to the transition layer between the enrichment aera and the rest of the domain leads to consider a pointwise matching condition at the boundary of the subdomain. An optimal numerical rate of convergence is then obtained using such a nonconformal method

Résultat de convergence quasi-optimal en mécanique de la rupture avec XFEM

International audienceThe aim of this Note is to give a convergence result for a variant of the eXtended Finite Element Method (XFEM) on cracked domains using a cut-off function to localize the singular enrichment area. The difficulty is caused by the discontinuity of the displacement field across the crack, but we prove that a quasi-optimal convergence rate holds in spite of the presence of elements cut by the crack. The global linear convergence rate is obtained by using an enriched linear finite element method.Le but de cette Note est de donner un résultat de convergence pour une variante de la méthode XFEM (eXtended Finite Element Method) sur un domaine fissuré en utilisant une fonction cut-off pour localiser l'enrichissement par les fonctions singulières. La difficulté est causée par la discontinuité du champ de déplacement à travers la fissure, mais on montre une convergence quasi-optimale malgré la présence d'éléments coupés par la fissure. Le résultat de convergence globale linéaire est obtenu en utilisant une méthode d'éléments finis affines enrichis

A quasi-optimal convergence result for fracture mechanics with XFEM

International audienceThe aim of this Note is to give a convergence result for a variant of the eXtended Finite Element Method (XFEM) on cracked domains using a cut-off function to localize the singular enrichment area. The difficulty is caused by the discontinuity of the displacement field across the crack, but we prove that a quasi-optimal convergence rate holds in spite of the presence of elements cut by the crack. The global linear convergence rate is obtained by using an enriched linear finite element method

Operative management of acute abdomen after bariatric surgery in the emergency setting: the OBA guidelines

Background: Patients presenting with acute abdominal pain that occurs after months or years following bariatric surgery may present for assessment and management in the local emergency units. Due to the large variety of surgical bariatric techniques, emergency surgeons have to be aware of the main functional outcomes and long-term surgical complications following the most performed bariatric surgical procedures. The purpose of these evidence-based guidelines is to present a consensus position from members of the WSES in collaboration with IFSO bariatric experienced surgeons, on the management of acute abdomen after bariatric surgery focusing on long-term complications in patients who have undergone laparoscopic sleeve gastrectomy and laparoscopic Roux-en-Y gastric bypass. Method: A working group of experienced general, acute care, and bariatric surgeons was created to carry out a systematic review of the literature following the Preferred Reporting Items for Systematic Review and Meta-analysis Protocols (PRISMA-P) and to answer the PICO questions formulated after the Operative management in bariatric acute abdomen survey. The literature search was limited to late/long-term complications following laparoscopic sleeve gastrectomy and laparoscopic Roux-en-Y gastric bypass. Conclusions: The acute abdomen after bariatric surgery is a common cause of admission in emergency departments. Knowledge of the most common late/long-term complications (> 4 weeks after surgical procedure) following sleeve gastrectomy and Roux-en-Y gastric bypass and their anatomy leads to a focused management in the emergency setting with good outcomes and decreased morbidity and mortality rates. A close collaboration between emergency surgeons, radiologists, endoscopists, and anesthesiologists is mandatory in the management of this group of patients in the emergency setting

Mathematical and numerical study of extended finite element method for fractured domains computations

Dans la première partie de cette thèse, on introduit deux variantes XFEM qui permettent d'obtenir des convergences optimales avec XFEM tout en réduisant le coût de calcul. La première, la méthode XFEM avec une fonction cutoff, consiste à introduire un enrichissement singulier globalisé au voisinage du fond de la fissure via une fonction de localisation. Dans la deuxième, l'enrichissement singulier est introduit globalement sur un sous domaine contenant le fond de fissure. Ensuite, ce sous domaine est raccordé avec le reste du domaine fissuré avec une condition faible de raccord intégral. Cette approche permet d'améliorer l'approximation par rapport à cutoff XFEM. La deuxième partie est dédiée à l'introduction de deux nouvelles variantes qui permettent d'étendre le champ d'applications de XFEM standard, tout en bénéficiant des avantages des méthodes proposées précédemment. La première, Spider XFEM, consiste à remplacer la dépendance en thêta de l'enrichissement singulier exact par une approximation éléments finis calculé sur un maillage circulaire adapté. Dans la deuxième, Reduced Basis XFEM, on utilise, comme enrichissement singulier, une approximation éléments finis de toute la singularité, réalisée sur un maillage raffiné d'un domaine fissuré. Contrairement à XFEM standard, ces deux dernières permettent d'utiliser XFEM dans des cas où l'expression de la singularité est partiellement ou totalement inconnue, voire très compliqué. On démontre des résultats mathématiques de convergence optimale pour les variantes proposées. On réalise aussi différents tests numériques qui valident les résultats théoriques obtenuesIn the first part of this thesis, we introduce two XFEM variants allowing to obtain optimal convergence results for XFEM with a reduced computational cost. The first one, the XFEM with a cutoff function, consists in the introduction of a globalized singular enrichment via a localization function around the crack tip. In the second variant, the singular enrichment is defined globally over a subdomain containing the crack tip. Then, this subdomain is bonded with the rest of the cracked domain using a weak integral matching condition. This approach enhances the approximation with respect to the first one. The second part is dedicated to the introduction of two other XFEM methods allowing to extend the application field of XFEM, while getting benefit of the advantages of the former variants. In the first one, the Spider XFEM, the dependence in theta of the exact singular enrichment is replaced by an approximation computed over an adapted circular mesh. Meanwhile, in the second approach, the reduced basis XFEM, an approximation of the whole singularity, computed on a very refined mesh of a cracked domain, is used as singular enrichment. These two variants allow to use XFEM in some cases when the singularity is partially or completely unknown, or even when it's exact expansion is complicated. We prove mathematical optimal convergence results for these approaches and we perform different numerical experiments that validate the theoretical studyTOULOUSE-INSA (315552106) / SudocSudocFranceF

Une amélioration dans X-FEM du raccord entre enrichissement et éléments finis classiques

International audienceOn s'intéresse au calcul des déformations d'un corps élastique fissuré par la méthode des éléments finis étendue. On sait que la qualité de l'approximation est perturbée par la couche des éléments finis de transition entre zone d'enrichissement autour du fond de fissure et le reste du maillage. On propose de remplacer la couche de transition par une condition intégrale, de type "raccord mortar", à l'interface entre ces deux zones. Nous montrerons comment cette variante de XFEM permet d'améliorer sensiblement la précision

A non-conformal eXtended Finite Element approach: Integral matching Xfem

International audienceThis work is dedicated to the mathematical and numerical analysis of a new Xfem approach: the integral maching Xfem. It is known that the quality of the approximation and the convergence rate of Xfem type methods is broadly influenced by the transition layer between the singular enrichment area and the rest of the domain. In the presented method, this transition layer is replaced by an interface associated with an integral matching condition of mortar type. We prove an optimal convergence result for such a non-conformal approximation method and we perform some numerical experiments showing the advantages of the integral matching Xfem with respect to former Xfem approaches

Spider-xfem, an extended finite element variant for partially unknown crack-tip displacement

International audienceIn this paper, we introduce a new variant of the extended finite element method (Xfem) allowing an optimal convergence rate when the asymptotic displacement is partially unknown at the crack tip. This variant consists in the addition of an adapted discretization of the asymptotic displacement. We give a mathematical result of quasi-optimal a priori error estimate which allows to analyze the potentialities of the method. Some computational tests are provided and a comparison is made with the classical Xfem.Dans cet article, nous introduisons une nouvelle variante de la méthode des éléments finis étendus (Xfem) permettant l’obtention d’un taux de convergence optimal lorsque le déplacement asymptotique en pointe de fissure est partiellement inconnu. Cette variante consiste en l’addition d’une discrétisation adaptée du déplacement asymptotique. Nous donnons un résultat mathématique d’estimation d’erreur a priori quasi optimal qui permet d’analyser les potentialités de la méthode. Des tests numériques sont présentés et une comparaison est faite avec la méthode Xfem classique

An improvement within XFEM of the bonding between the enrichment area and the classical finite elements

International audienceWe are interested in XFEM strain calculations of a cracked elastic body. It is already known that with XFEM, the approximation quality is distorted by the layer of elements lying between the singular enrichment area and the rest of the mesh. In the following work, we replace this transition layer by a "mortar" type integral bonding condition at the interface between the two areas. We prove how the proposed approach enhance significantly the approximation.On s’intéresse au calcul des déformations d’un corps élastique fissuré par la méthode des éléments finis étendue. On sait que la qualité de l’approximation est perturbée par la couche des éléments finis de transition entre la zone d’enrichissement autour du fond de fissure et le reste du maillage. On propose de remplacer la couche de transition par une condition intégrale, de type « raccord mortar », à l’interface entre ces deux zones. Nous montrons comment cette variante de XFEM permet d’améliorer sensiblement la précision