Stable algorithm for the stress field around a multiply branched crack

Research output: Contribution to journalArticle


We present an algorithm for the computation of the stress field around a branched crack. The algorithm is based on an integral equation with good numerical properties. Our equation is obtained through a left regularization of an integral equation of Fredholm's first kind. Complex valued functions involving repeated products of square roots appear in the regularization. A new and effective scheme for correct evaluation of these functions is described. For validation, mode I and II stress intensity factors are computed for simple branched geometries. The relative errors in the stress intensity factors are typically as low as 10(-12). A large scale example is also presented, where a crack with 176 branching points is studied.


  • Jonas Englund
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • fast multipole method, stress intensity factor, integral equation, branched crack
Original languageEnglish
Pages (from-to)926-946
JournalInternational Journal for Numerical Methods in Engineering
Issue number6
Publication statusPublished - 2005
Publication categoryResearch

Bibliographic note

The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)