### Abstract

We solve the homogeneous Eshelby inclusion problem on a finite unit cell with periodic boundary conditions. The main result is a representation formula of the strain field which is reminiscent of the familiar Green's representation formula. The formula is valid for any smooth inclusion and divergence-free eigenstress. More, it is shown that a Vigdergauz structure does not have the Eshelby uniformity property for symmetric non-dilatational eigenstress unless it degenerates to a laminate.

Original language | English (US) |
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Pages (from-to) | 557-590 |

Number of pages | 34 |

Journal | Mathematics and Mechanics of Solids |

Volume | 15 |

Issue number | 5 |

DOIs | |

State | Published - Jul 1 2010 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Materials Science(all)
- Mechanics of Materials

### Keywords

- Complex variable method
- Eshelby inclusion problem
- Periodic inclusions