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Stochastic Computational Mechanics in Brittle Fracture and Fatigue

  • Conference paper
Nonlinear Stochastic Mechanics

Part of the book series: IUTAM Symposia ((IUTAM))

Abstract

The probabilistic finite element method (PFEM), which is based on a second-order perturbation is developed for non-linear problems. In order to incorporate the probabilistic distribution for the compatibility condition, constitutive law, equilibrium, domain, and boundary conditions into the PFEM, the probabilistic Hu-Washizu variational principal is applied. The first- and second- order moments of the response variable are determined from the statistics of the random parameters and loads. The fusion of the PFEM and the first order reliability analysis provides a means for determining fatigue life and its stochastic nature which results from the randomness in the load, crack length, crack location and orientation, and crack growth parameters. A stochastic damage model is employed to explore the brittle fracture of advanced materials. The model, based on the macrocrack-microcrack interaction, incorporates uncertainties in locations and orientations of microcracks. The statistical nature of the fracture toughness is compared with the Neville function, which gives correct fits to sets of experimental data from advanced materials. Finally, a stochastic approach to the curved fatigue crack growth reliability is outlined.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Northwestern University, Evanston, Illinois, USA

    W. K. Liu (Professor), Y. J. Lua (Post-Doctoral Fellow) & T. Belytschko (Professor)

Authors
  1. W. K. Liu
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  2. Y. J. Lua
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  3. T. Belytschko
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129, Torino, Italy

    Nicola Bellomo

  2. Dept. of Structural Mechanics, University of Pavia, Via Abbiategrasso 211, I-27100, Pavia, Italy

    Fabio Casciati

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© 1992 Springer-Verlag Berlin Heidelberg

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Liu, W.K., Lua, Y.J., Belytschko, T. (1992). Stochastic Computational Mechanics in Brittle Fracture and Fatigue. In: Bellomo, N., Casciati, F. (eds) Nonlinear Stochastic Mechanics. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84789-9_31

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  • DOI: https://doi.org/10.1007/978-3-642-84789-9_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-84791-2

  • Online ISBN: 978-3-642-84789-9

  • eBook Packages: Springer Book Archive

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