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Stochastic multiscale modeling of crack propagation in random heterogeneous media

Publication ,  Journal Article
Hun, DA; Guilleminot, J; Yvonnet, J; Bornert, M
Published in: International Journal for Numerical Methods in Engineering
September 28, 2019

A stochastic approach to model crack propagation in random heterogeneous media, using mesoscopic representations of elastic and fracture properties, is presented. In order to obtain reference results, Monte-Carlo simulations are first conducted on microstructural samples in which a pre-existing crack is propagated by means of a phase-field approach. These computations are used to estimate the subscale-induced randomness on the macroscopic response of the domain. Mesoscopic descriptors are then introduced to investigate scale transition. Elasticity tensor random fields are specifically defined, at that stage, through a moving-window upscaling approach. The mesoscopic fracture toughness, which is assumed homogeneous and deterministic, is identified by solving an inverse problem involving the macroscopic peak force. A stochastic model is subsequently constructed in which the mesoscopic elasticity is described as a non-Gaussian random field. This model allows the multiscale-informed elastic counterpart in the phase-field formulation to be sampled without resorting to computational homogenization. The results obtained with the sample-based and model-based mesoscopic descriptions are finally compared with those corresponding to the full-scale microscopic model. It is shown, in particular, that the mesoscopic elasticity-phase-field formulation associated with statically uniform boundary conditions enables the accurate predictions of the mean elastic response and mean peak force.

Duke Scholars

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

September 28, 2019

Volume

119

Issue

13

Start / End Page

1325 / 1344

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering
 

Citation

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Hun, D. A., Guilleminot, J., Yvonnet, J., & Bornert, M. (2019). Stochastic multiscale modeling of crack propagation in random heterogeneous media. International Journal for Numerical Methods in Engineering, 119(13), 1325–1344. https://doi.org/10.1002/nme.6093
Hun, D. A., J. Guilleminot, J. Yvonnet, and M. Bornert. “Stochastic multiscale modeling of crack propagation in random heterogeneous media.” International Journal for Numerical Methods in Engineering 119, no. 13 (September 28, 2019): 1325–44. https://doi.org/10.1002/nme.6093.
Hun DA, Guilleminot J, Yvonnet J, Bornert M. Stochastic multiscale modeling of crack propagation in random heterogeneous media. International Journal for Numerical Methods in Engineering. 2019 Sep 28;119(13):1325–44.
Hun, D. A., et al. “Stochastic multiscale modeling of crack propagation in random heterogeneous media.” International Journal for Numerical Methods in Engineering, vol. 119, no. 13, Sept. 2019, pp. 1325–44. Scopus, doi:10.1002/nme.6093.
Hun DA, Guilleminot J, Yvonnet J, Bornert M. Stochastic multiscale modeling of crack propagation in random heterogeneous media. International Journal for Numerical Methods in Engineering. 2019 Sep 28;119(13):1325–1344.
Journal cover image

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

September 28, 2019

Volume

119

Issue

13

Start / End Page

1325 / 1344

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering