## Mathematical theory of dislocations |

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### Contents

Introduction to the Mathematical Theory of Dislocations | 1 |

Method of Continuously Distributed Dislocations | 25 |

Dislocations in Anisotropic Elastic Media | 49 |

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### Common terms and phrases

A. K. Head Acta antiplane Appl applied stress atoms axis behavior Burgers vector CIRCULAR INCLUSION climbing edge dislocation configuration considered continuous distribution continuum continuum theory cosh crack curve deformation discrete dislocations dislocation line dislocation loop dislocation moves dislocation pile-ups dislocation theory dislocation-distribution function Dislocations in Anisotropic displacement distribution of dislocations elastic constants elastic fields Equation equilibrium position finite given glide plane gliding edge dislocation infinite inhomogeneities integral interaction energy interface isotropic isotropic materials J. D. Eshelby L. J. Teutonico layer linear-elastic longitudinal wave medium Mura number of dislocations obtained periodic force law Phil Phys plane strain plastic Poisson's ratio problem Proc Rayleigh wave screw dislocation segment self-energy sextic equation shear modulus shear stress shear wave shown in Fig single-ended pile-ups solution straight dislocations strain stress field stress function supersonic dislocation tensor Theory of Dislocations tion transonic unstable wave velocity Weertman Y. T. Chou zero