A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. (English) Zbl 1161.74054

Summary: This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for nonlinear 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.


74S30 Other numerical methods in solid mechanics (MSC2010)
74R20 Anelastic fracture and damage
74R10 Brittle fracture
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