### Abstract

The effective moduli of a composite medium containing many randomly positioned and oriented elliptical objects is calculated and the results are applied to the case of voids. Two different self-consistent effective medium approximations are described. The asymmetric self-consistent method shows that the Young's modulus E* goes to zero as E* equals E//1 (p minus p//c)/(1 minus p//c), where phi equals 1 minus p is the concentration of the voids. The subscript 1 denotes the void free material. The Poisson ratio sigma is also linear in p and goes to a value sigma //c at p//c that is independent of the initial value of Poisson's ratio sigma . The two elastic moduli decouple in this case. The corresponding elastic threshold is p//c equals left bracket 1 plus ab/(a**2 plus b**2) right bracket ** minus **1, where a and b are the major semi-axes. The symmetric self-consistent method yields a different p//c equals 2 left bracket 1 plus ROOT 2(a plus b)**2/(a**2 plus b**2) right bracket ** minus **1 and a different concentration dependence of the effective moduli. Both methods give the same result for circular inclusions and both methods give p//c plus sigma //c equals 1 for all aspect ratios.

Original language | English (US) |
---|---|

Title of host publication | Proceedings - The Electrochemical Society |

Editors | Micha Tomkiewicz, P.N. Sen |

Publisher | Electrochemical Soc |

Pages | 328-335 |

Number of pages | 8 |

Volume | 85-8 |

State | Published - 1985 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings - The Electrochemical Society*(Vol. 85-8, pp. 328-335). Electrochemical Soc.

**ELASTIC MODULI OF TWO DIMENSIONAL ELASTIC CONTINUA WITH ELLIPTICAL HOLES.** / Sen, P. N.; Thorpe, Michael.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - The Electrochemical Society.*vol. 85-8, Electrochemical Soc, pp. 328-335.

}

TY - GEN

T1 - ELASTIC MODULI OF TWO DIMENSIONAL ELASTIC CONTINUA WITH ELLIPTICAL HOLES.

AU - Sen, P. N.

AU - Thorpe, Michael

PY - 1985

Y1 - 1985

N2 - The effective moduli of a composite medium containing many randomly positioned and oriented elliptical objects is calculated and the results are applied to the case of voids. Two different self-consistent effective medium approximations are described. The asymmetric self-consistent method shows that the Young's modulus E* goes to zero as E* equals E//1 (p minus p//c)/(1 minus p//c), where phi equals 1 minus p is the concentration of the voids. The subscript 1 denotes the void free material. The Poisson ratio sigma is also linear in p and goes to a value sigma //c at p//c that is independent of the initial value of Poisson's ratio sigma . The two elastic moduli decouple in this case. The corresponding elastic threshold is p//c equals left bracket 1 plus ab/(a**2 plus b**2) right bracket ** minus **1, where a and b are the major semi-axes. The symmetric self-consistent method yields a different p//c equals 2 left bracket 1 plus ROOT 2(a plus b)**2/(a**2 plus b**2) right bracket ** minus **1 and a different concentration dependence of the effective moduli. Both methods give the same result for circular inclusions and both methods give p//c plus sigma //c equals 1 for all aspect ratios.

AB - The effective moduli of a composite medium containing many randomly positioned and oriented elliptical objects is calculated and the results are applied to the case of voids. Two different self-consistent effective medium approximations are described. The asymmetric self-consistent method shows that the Young's modulus E* goes to zero as E* equals E//1 (p minus p//c)/(1 minus p//c), where phi equals 1 minus p is the concentration of the voids. The subscript 1 denotes the void free material. The Poisson ratio sigma is also linear in p and goes to a value sigma //c at p//c that is independent of the initial value of Poisson's ratio sigma . The two elastic moduli decouple in this case. The corresponding elastic threshold is p//c equals left bracket 1 plus ab/(a**2 plus b**2) right bracket ** minus **1, where a and b are the major semi-axes. The symmetric self-consistent method yields a different p//c equals 2 left bracket 1 plus ROOT 2(a plus b)**2/(a**2 plus b**2) right bracket ** minus **1 and a different concentration dependence of the effective moduli. Both methods give the same result for circular inclusions and both methods give p//c plus sigma //c equals 1 for all aspect ratios.

UR - http://www.scopus.com/inward/record.url?scp=0022235129&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022235129&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0022235129

VL - 85-8

SP - 328

EP - 335

BT - Proceedings - The Electrochemical Society

A2 - Tomkiewicz, Micha

A2 - Sen, P.N.

PB - Electrochemical Soc

ER -