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A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement

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Abstract

We propose an alternative crack propagation algorithm which effectively circumvents the variable transfer procedure adopted with classical mesh adaptation algorithms. The present alternative consists of two stages: a mesh-creation stage where a local damage model is employed with the objective of defining a crack-conforming mesh and a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation which is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered scheme for standard equilibrium and screened Poisson equations is used in this second stage. Element subdivision is based on edge split operations using a constitutive quantity (damage). To assess the robustness and accuracy of this algorithm, we use five quasi-brittle benchmarks, all successfully solved.

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Authors and Affiliations

  1. Department of Physics, University of Évora, Colégio Luís António Verney Rua Romão Ramalho, 59, 7002-554, Évora, Portugal

    P. Areias

  2. Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße 15, 99423, Weimar, Germany

    T. Rabczuk

  3. Mechanical Engineering, Department Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal

    J. César de Sá

  4. CERIS/Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    P. Areias

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  1. P. Areias
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  3. J. César de Sá
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Correspondence to P. Areias.

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Areias, P., Rabczuk, T. & de Sá, J.C. A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement. Comput Mech 58, 1003–1018 (2016). https://doi.org/10.1007/s00466-016-1328-5

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