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Probabilistic dipole BEM model for cohesive crack propagation analysis

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Abstract

This paper addresses the application of the boundary element method (BEM) to plane problems in probabilistic fracture mechanics. BEM stands out as an interesting technique for crack propagation analysis, leading to a robust modelling of stress concentration in singular regions, besides attenuating remeshing aspects. The alternative BEM formulation employed herein is built in terms of a set of self-equilibrated forces, called dipole, which describes the cohesive zone. Regarding the nonlinear solution, the tangent operator is used to make it faster. The probabilistic assessment of the crack propagation analysis is carried out in two stages: the first consists of a simulation-based estimation of the random values of cohesive parameters and elastic modulus, by an inferential approach; and in the second, the influence of these parameters on the structural response is evaluated. The statistical correlation between the random variables is taken into account. BEM models are coupled to structural reliability routines based on both first-order reliability method and Latin hypercube sampling-based Monte Carlo simulation to compute failure probabilities and random force versus displacement and crack path curves. Some examples are presented to validate the proposed models and to illustrate their efficacy on the reliability-based assessment of cohesive crack modelling.

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Acknowledgements

The authors are grateful to the Coordination for the Improvement of Higher Education Personnel – CAPES, for the scholarship provided to the first author.

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Authors and Affiliations

  1. Department of Structural Engineering, University of São Paulo, São Carlos, SP, Brazil

    Luís Philipe Ribeiro Almeida

  2. Laboratory of Scientific Computing and Visualization, Federal University of Alagoas, Maceió, AL, Brazil

    Eduardo Toledo de Lima Junior & João Carlos Cordeiro Barbirato

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  1. Luís Philipe Ribeiro Almeida
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  2. Eduardo Toledo de Lima Junior
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  3. João Carlos Cordeiro Barbirato
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Correspondence to Eduardo Toledo de Lima Junior.

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Almeida, L.P.R., de Lima Junior, E.T. & Barbirato, J.C.C. Probabilistic dipole BEM model for cohesive crack propagation analysis. J Braz. Soc. Mech. Sci. Eng. 44, 485 (2022). https://doi.org/10.1007/s40430-022-03765-8

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