Résumé :Nous présentons une approche prometteuse afin de réduire les difficultés liées aux maillages de géométries avec frontières courbes pour l'analyse avec deséléments finis d'ordre supérieur. Une analyse par XFEM d'ordre supérieur dans le cas de la modélisation des interfaces matériau-vide est testée sur un ensemble représentatif de problèmes d'élasticité linéaire. Les frontières implicites courbes sont approximéesà l'intérieur d'un maillage grossier non structuré en utilisant les informations paramétriques extraites de la représentation paramétrique (la plus populaire en conception CAO). Cette approximation génère un sous-maillage gradué (SMG)à l'intérieur deséléments traversés par la frontière qui sera utiliséà des fins d'intégrations numérique. Exemples de géométries et des expériences numériques illustrent la précision et la robustesse de l'approche proposée.
Abstract :We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong discontinuity in the case of linear elasticity problems are presented. Curved implicit boundaries are approximated inside an unstructured coarse mesh by using parametric information extracted from the parametric representation (the most common in Computer Aided Design CAD). This approximation provides local graded sub-mesh (GSM) inside boundary elements (i.e. an element split by the curved boundary) which will be used for integration purpose. Sample geometries and numerical experiments illustrate the accuracy and robustness of the proposed approach.
The rubbery environments present the same mechanical behaviour as hyperelastic or viscohyperelastic material. Regarding the filled-elastomers, the high degree of deformability often generate microscopic and voluminal defects leading to the creation of micro-cracks inside the structure. It is important to develop sophisticated models to take into account the various physical phenomena and particularly the degradation of the matter by damage (or Mullins effect). The proposed approach is used to couple material degradation by damage with permanent strain in filled-elastomer materials. The efficiency of the method is validate with some examples.
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