Abstract
This paper summarizes the development of the surface integral and finite element hybrid method for two and three dimensional fracture mechanics analysis. The fracture, which is a discontinuity in the displacement field, is modeled explicitly and efficiently by use of dislocations for two dimensional analysis and by dipoles of point forces for three dimensional applications. The boundary value problem of a fracture in a finite domain is solved by (incremental) superposition of a finite element model of the finite body without the crack and a surface integral model of an infinite body with the crack, ensuring proper traction and displacement matching at the boundaries. Finite elements are also used to model nonhomogeneity and plasticity, though isotropic kernels are used for the integral equation. A variety of two and three dimensional problems have been modeled and excellent agreement with analytical solutions has been obtained. Propagation problems in two dimensions have also been modeled and the predicted results agree very well with experimental observations.
Résumé
On résume le développement de la méthode de l'intégrale de surface et des éléments finis hybrides pour l'analyse de la mécanique de rupture à deux et à trois dimensions. La rupture, considérée comme une discontinuité dans un champ de déplacement, est représentée de manière explicite et avec efficience en recourant aux dislocations dans le cas de l'analyse à deux dimensions, et aux dipoles de forces ponctuelles dans le cas des applications à trois dimensions. Le problème de la valeur aux limites d'une rupture dans un domaine fini est solutionné par la superposition par incréments d'un modèle à éléments finis d'un corps fini dépourvu de fissures et d'un modèle en intégrale de surface d'un corps infini pourvu d'une fissure, en s'assurant que les conditions appropriées de traction et de déplacement s'accordent aux limites. On utilise également les éléments finis pour représenter une non homogénité ou de la plasticité, bien que des kernels isotropes soient employés pour l'équation intégrale. On a représenté divers problèmes à deux et à trois dimensions et on a obtenu un excellent accord avec les solutions analytiques. Les problèmes de propagation en deux dimensions ont également été modélisés, et ces résultats prévus sont en excellent accord avec les observations expérimentales.
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Keat, W.D., Annigeri, B.S. & Cleary, M.P. Surface integral and finite element hybrid method for two- and three-dimensional fracture mechanics analysis. Int J Fract 36, 35–53 (1988). https://doi.org/10.1007/BF00034816
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DOI: https://doi.org/10.1007/BF00034816