The interaction between a penny-shaped crack and a spherical inclusion under torsion

  • Yuri A. Godin
Original Papers


The axisymmetric interaction problem of an elastic spherical inclusion with a penny-shaped crack in an elastic space under torsion is considered. The superposition and reflection methods [3]-[4] are used to solve the mixed boundary value problem in question. With the help of the dual integral equations technique and appropriate re-expansion of the eigenfunction, the problem is reduced to an infinite system of linear algebraic equations of the second kind. The matrix elements of that system decrease exponentially along the rows and the columns. Its unique solution is proved to exist in a proper class of sequences and is shown to be represented by a convergent, in the vicinity of the origin, power series in a geometric parameter, equal to the ratio of the radius of the inclusion to its distance from the crack. This procedure provides an efficient formula for the stress intensity factor.


Stress Intensity Intensity Factor Stress Intensity Factor Power Series Linear Algebraic Equation 
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Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Yuri A. Godin
    • 1
  1. 1.Dept of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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