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A constitutive-based element-by-element crack propagation algorithm with local mesh refinement

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Abstract

In the context of multiple constitutive models, multiple finite element formulations and crack nucleation and propagation hypotheses, we propose a simple yet effective algorithm to initiate and propagate cracks in 2D models which is independent of the constitutive and element specific technology. Observed phenomena such as multiple crack growth and shielding emerge naturally, without specialized algorithms for calculating the crack growth direction. The algorithm consists of a sequence of mesh subdivision, mesh smoothing and element erosion steps. Element subdivision is based on the classical edge split operations using a given constitutive quantity (either damage or void fraction). Mesh smoothing makes use of edge contraction as function of a given constitutive quantity (such as void fraction or principal stress). To assess the robustness and accuracy of this algorithm, we use classical quasi-brittle benchmarks and ductile tests.

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Notes

  1. No power-consistent closed-form solution exists for the effective plastic strain in the classical Gurson model.

  2. Note that properties have been fitted so that intersections in p and q axes for both models coincide at \(f=f_{c}.\)

    Fig. 22
    figure 22

    Effective plastic strain and void nucleation and growth in the GTN and Rousselier models

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    Fig. 23
    figure 23

    Aluminum specimen, GTN and Rousselier models with remeshing, mesh size sensitivity: effective plastic strain, void fraction and reaction-displacement results. Step size \(\Delta \overline{v}=0.09\) mm. Experimental data reported by Malcher et al. [31]

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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. Group of Elasticity and Strength of Materials, School of Engineering, University of Seville, Camino de los Descubrimientos s/n, 41092, Seville, Spain

    J. Reinoso

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

    P. Camanho

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

    T. Rabczuk

  5. ICIST, Instituto Superior Técnico, Lisbon, Portugal

    P. Areias

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  1. P. Areias
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Correspondence to P. Areias.

Additional information

P. Areias: Researcher ID: A-8849-2013

http://www.researcherid.com/rid/A-8849-2013.

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Areias, P., Reinoso, J., Camanho, P. et al. A constitutive-based element-by-element crack propagation algorithm with local mesh refinement. Comput Mech 56, 291–315 (2015). https://doi.org/10.1007/s00466-015-1172-z

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  • DOI: https://doi.org/10.1007/s00466-015-1172-z

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