A three dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics (2007)
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.
CitationRabczuk, T., Bordas, S., Zi, G. (2007) A three dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 40(3), pp. 473-495.
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Keywordsextended element free Galerkin method (XEFG); three dimensional cracks; cohesive forces; static and dynamic fracture; extrinsic partition of unity enrichment; non-linear fracture mechanics
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Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment Bordas, S.; Rabczuk, T.; Zi, G. (University of Canterbury. Mechanical Engineering., 2008)This paper presents a three-dimensional, extrinsically enriched meshfree method for initiation, branching, growth and coalescence of an arbitrary number of cracks in non-linear solids including large deformations, for ...
Zi, G.; Rabczuk, T.; Wall, W.A. (University of Canterbury. Mechanical Engineering., 2007)An extended meshless method for both static and dynamic cohesive cracks is proposed. This new method does not need any crack tip enrichment to guarantee that the crack closes at the tip. All cracked domains of influence ...
Rabczuk, T.; Zi, G. (University of Canterbury. Mechanical Engineering., 2007)We will present a meshfree method based on the local partition of unity for cohesive cracks. The cracks are described by a jump in the displacement field for particles whose domain of influence is cut by the crack. Particles ...