## Abstract

The elastic field around an elliptical inclusion in two dimensions is obtained. This result is then used to compute the effective moduli of a composite medium containing many randomly positioned and oriented elliptical objects. Two different self-consistent methods are described and the special cases of voids and rigid reinforcement are considered in detail. The asymmetric self-consistent method shows that the Young’s modulus E goes to zero as E = E_{1}(p − p_{c})/(1 − p_{c}), where 1 − p is the concentration of the voids and subscript one denotes the void free material. The Poisson ratio σ is also linear inp and goes to a value σ_{c} at p_{c} that is independent of the initial value of Poisson’s ratio σ_{1}. Unlike the corresponding three-dimensional case, the two elastic moduli decouple in this special case. The corresponding elastic threshold is p_{c} = √2(a + b)^{2}/(a^{2}+b^{1})]^{-1}, where a and b are the major semiaxes. The symmetric self-consistent method yields a different [1 + ab /(a^{2} + b^{2})] and a different concentration dependence of the effective moduli. Both methods give the same result for circular inclusions and both methods give p_{c} + σ_{c} = 1 for all aspect ratios. Similar results are presented for the case of rigid reinforcements.

Original language | English (US) |
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Pages (from-to) | 1674-1680 |

Number of pages | 7 |

Journal | Journal of the Acoustical Society of America |

Volume | 77 |

Issue number | 5 |

DOIs | |

State | Published - May 1985 |

Externally published | Yes |

## ASJC Scopus subject areas

- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics