Multiscale aggregating discontinuities: A method for circumventing loss of material stability

Authors

  • Ted Belytschko,

    Corresponding author
    1. Theoretical and Applied Mechanics, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, U.S.A.
    • Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, U.S.A.
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    • Walter P. Murphy and McCormick Professor.

  • Stefan Loehnert,

    1. Institute of Mechanics and Computational Mechanics, Leibniz University Hannover, Appelstr. 9A, 30167 Hannover, Germany
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    • Research Associate.

  • Jeong-Hoon Song

    1. Theoretical and Applied Mechanics, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, U.S.A.
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    • Graduate Research Assistant.


Abstract

New methods for the analysis of failure by multiscale methods that invoke unit cells to obtain the subscale response are described. These methods, called multiscale aggregating discontinuities, are based on the concept of ‘perforated’ unit cells, which exclude subdomains that are unstable, i.e. exhibit loss of material stability. Using this concept, it is possible to compute an equivalent discontinuity at the coarser scale, including both the direction of the discontinuity and the magnitude of the jump. These variables are then passed to the coarse-scale model along with the stress in the unit cell. The discontinuity is injected at the coarser scale by the extended finite element method. Analysis of the procedure shows that the method is consistent in power and yields a bulk stress–strain response that is stable. Applications of this procedure to crack growth in heterogeneous materials are given. Copyright © 2007 John Wiley & Sons, Ltd.

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