A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

Timon Rabczuk, Stéphane Bordas, Goangseup Zi

    Research output: Contribution to journalArticlepeer-review

    323 Citations (Scopus)

    Abstract

    This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is based on a local partition of unity. An extrinsic enrichment of the meshfree shape functions is used with discontinuous and near-front branch functions to close the crack front and improve accuracy. The crack is hereby modeled as a jump in the displacement field. The initiation and propagation of a crack is determined by the loss of hyperbolicity or the loss of material stability criterion. The method is applied to several static, quasi-static and dynamic crack problems. The numerical results very precisely replicate available experimental and analytical results.

    Original languageEnglish
    Pages (from-to)473-495
    Number of pages23
    JournalComputational Mechanics
    Volume40
    Issue number3
    DOIs
    Publication statusPublished - 2007 Aug

    Keywords

    • Cohesive forces
    • Extended element-free Galerkin method (XEFG)
    • Extrinsic partition of unity enrichment
    • Non-linear fracture mechanics
    • Static and dynamic fracture
    • Three-dimensional cracks

    ASJC Scopus subject areas

    • Computational Mechanics
    • Ocean Engineering
    • Mechanical Engineering
    • Computational Theory and Mathematics
    • Computational Mathematics
    • Applied Mathematics

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