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

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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.

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Authors and Affiliations

  1. Institute for Numerical Mechanics, Technical University of Munich, Boltzmannstr. 15, 85748, Garching b. Munich, Germany

    Timon Rabczuk

  2. Ecole Polytechnique Fédérale de Lausanne (EPFL) Laboratoire de structures et de mécanique des milieux continus, Station 18, 1015, Lausanne, Switzerland

    Stéphane Bordas

  3. Department of Civil and Environmental Engineering, Korea University, 5-1, Anam-dong, Sungbuk-Ku, Seoul, 136-701, South Korea

    Goangseup Zi

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  1. Timon Rabczuk
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  2. Stéphane Bordas
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  3. Goangseup Zi
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Correspondence to Timon Rabczuk.

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Rabczuk, T., Bordas, S. & Zi, G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Comput Mech 40, 473–495 (2007). https://doi.org/10.1007/s00466-006-0122-1

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