Domain decomposition and multi-scale computations of singularities in mechanical structures
type: Dataset
description: A major issue in fracture mechanics is to model the nucleation of a crack in a sound material. There are two difficulties: the first one is to propose a law able to predict that nucleation; the second is a purely numerical issue. It is indeed difficult to compute with a good accuracy all the mechanical quantities like the energy release rate associated with a crack of small length which appears at the tip of a notch. The classical finite element method leads to inaccurate results because of the overlap of two singularities which cannot be correctly captured by this method: one due to the tip of the notch, the other due to the tip of the crack. A specific method of approximation based on asymptotic expansions is preferable as it is developed in analog situations with localized defects. The first chapter of the thesis is devoted to the presentation of this Matched Asymptotic Method (shortly, the MAM) in the case of a defect (which includes the case of a crack) located at the tip of a notch in the simplified context of antiplane linear elasticity. The main goal of the thesis is to use these asymptotic methods to predict the nucleation or the propagation of defects (like cracks) near those singular points. The second chapter of the thesis will be devoted to this task. This requires, of course, to overcome the first issue by introducing a criterion for nucleation. This delicate issue has not received a definitive answer at the present time and it was considered for a long time as a problem which could not be solved in the framework of Griffith theory of fracture. The main invoked reason is that the release of energy due to a small crack tends to zero when the length of the crack tends to zero. Therefore, if one follows the Griffith criterion which stands that the crack can propagate only when the energy release rate reaches a critical value characteristic of the material, no nucleation is possible because the energy release rate vanishes when there is no preexisting crac…
issued: 2026-05-09T19:20:43.025321
language: en
modified: 2026-05-09T19:20:43.025326
contact point: Organization
  fn: CCSD
keyword: asymptotic-methods
keyword: brittle-fracture
keyword: cohesive-model
keyword: decomposition-de-domaines
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mecanique-de-la-rupture
keyword: methodes-asymptotiques
keyword: physmecasolidphysics-physicsmechanics-physicssolid-mechanics-physicsclass-ph
keyword: singularites
keyword: singularities
keyword: spimecasolidengineering-sciences-physicsmechanics-physicsmed-phsolid-mechanics-physicsc
keyword: theses
landing page: https://theses.hal.science/tel-00860371

Domain decomposition and multi-scale computations of singularities in mechanical structures
type: Distribution
format: HTML
issued: 2026-05-09T19:20:43.031807
modified: 2026-05-09T19:20:43.012828
access URL: https://theses.hal.science/tel-00860371

test_moissonnage_selune
type: Agent