### 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

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

### Cite this

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*Mathematics and Mechanics of Solids*, vol. 15, no. 5, pp. 557-590. https://doi.org/10.1177/1081286509104492

**Solutions to the periodic eshelby inclusion problem in two dimensions.** / Liu, Liping.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Solutions to the periodic eshelby inclusion problem in two dimensions

AU - Liu, Liping

PY - 2010/7/1

Y1 - 2010/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77955830322&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955830322&partnerID=8YFLogxK

U2 - 10.1177/1081286509104492

DO - 10.1177/1081286509104492

M3 - Article

VL - 15

SP - 557

EP - 590

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

SN - 1081-2865

IS - 5

ER -