DYNAMIC FRACTURE USING ELEMENT-FREE GALERKIN METHODS

Authors

  • T. BELYTSCHKO,

    Corresponding author
    1. Department of Civil Engineering, Robert R. McCormick School of Engineering and Applied Science, The Technological Institute, Northwestern University, Evanston, IL 60208-3109, U.S.A.
    • Department of Civil Engineering, Robert R. McCormick School of Engineering and Applied Science, The Technological Institute, Northwestern University, Evanston, IL 60208-3109, U.S.A.
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  • M. TABBARA

    1. Department of Civil Engineering, Robert R. McCormick School of Engineering and Applied Science, The Technological Institute, Northwestern University, Evanston, IL 60208-3109, U.S.A.
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Abstract

The element-free Galerkin method for dynamic crack propagation is described and applied to several problems. This method is a gridless method, which facilitates the modelling of growing crack problems because it does not require remeshing; the growth of the crack is modelled by extending its surfaces. The essential feature of the method is the use of moving least-squares interpolants for the trial-and-test functions. In these interpolants, the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point. The discrete equations are obtained by a Galerkin method. The procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described.

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