## Abstract

The present study is devoted to application of boundary integral equations to the problem for interface cracks located between two dissimilar homogeneous isotropic half-spaces under time-harmonic loading. The detailed procedure for deriving the system of boundary integral equations from the Somigliana dynamic identity is given. The integrals of hypersingular and singular kernels are regularised and computed.

The opposite faces of existing cracks interact with each other under deformation, affecting significantly the stress and strain fields. Unfortunately, due to substantial complications in solution researchers almost always neglect the contact interaction of crack faces in spite of its evident significance.

In order to take the contact interaction of crack faces into account we assume there is no interpenetration of the opposite crack faces and the contact force is unilateral. Thus the Signorini constraints are imposed for normal components of displacements and forces. We also assume that the contact interaction satisfies the Coulomb friction law. The solution is refined during the iteration process until the distribution of physical values satisfy the contact constraints. The results are compared with those obtained without allowance for the contact interaction.

The opposite faces of existing cracks interact with each other under deformation, affecting significantly the stress and strain fields. Unfortunately, due to substantial complications in solution researchers almost always neglect the contact interaction of crack faces in spite of its evident significance.

In order to take the contact interaction of crack faces into account we assume there is no interpenetration of the opposite crack faces and the contact force is unilateral. Thus the Signorini constraints are imposed for normal components of displacements and forces. We also assume that the contact interaction satisfies the Coulomb friction law. The solution is refined during the iteration process until the distribution of physical values satisfy the contact constraints. The results are compared with those obtained without allowance for the contact interaction.

Original language | English |
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Pages | 65 |

Number of pages | 1 |

Publication status | Published - 2009 |

Event | British Applied Mathematics Colloquium 2009 incorporating British Theoretical Mechanics Colloquium - University of Nottingham, Nottingham, United Kingdom Duration: 7 Apr 2009 → 9 Apr 2009 Conference number: 51 http://www.personal.soton.ac.uk/~cjh/BAMC09/ |

### Conference

Conference | British Applied Mathematics Colloquium 2009 incorporating British Theoretical Mechanics Colloquium |
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Abbreviated title | BAMC / BTMC 2009 |

Country | United Kingdom |

City | Nottingham |

Period | 7/04/09 → 9/04/09 |

Internet address |