Alternative Integration Approaches in the Weight Function ‎Method for Crack Problems

Martin A. Eder, Xiao Chen*

*Corresponding author for this work

    Research output: Contribution to journalJournal articleResearchpeer-review

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    This study proposes two alternative approaches to complement existing integration strategies used in the weight function method for linear elastic crack problems. The first approach is based on an interpolation type integration scheme and the second approach is based on Gauss quadrature. The proposed approaches enable a computationally efficient numerical integration for computing stress intensity factors in 2D fracture problems. The efficiency is gained through a comparatively low number of integration points facilitated by higher-order approximation. The integration weights only need to be computed once for a given crack length-to-width ratio and can be applied to arbitrary continuous and smooth stress distributions. The proposed approaches show excellent accuracy. In particular, the Gauss quadrature approach exhibits several orders of magnitude more accuracy compared to the most commonly used trapezoidal integration.
    Original languageEnglish
    JournalJournal of Applied and Computational Mechanics
    Issue number3
    Pages (from-to)1719-1725
    Number of pages7
    Publication statusPublished - 2021


    • Stress intensity factor
    • Fracture mechanics
    • Crack length
    • Singularity
    • Weight function integration


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