### Abstract

The existence of diagonal symmetry in estimates of overall stiffness tensors of heterogeneous media is examined for several micromechanical models. The dilute approximation gives symmetric estimates for all matrix-based multiphase media. The Mori-Tanaka and the self-consistent methods do so for all two-phase systems, but only for those multiphase systems where the dispersed inclusions have a similar shape and alignment. However, the differential schemes associated with the self-consistent method can predict diagonally symmetric overall stiffness and compliance for multiphase systems of arbitrary phase geometry. A related question is raised about the equivalence of two possible approaches to evaluation of the overall thermal stress and strain tensors. A direct estimate follows from each of the above models, whereas Levin's results [Mechanics of Solids 2, 58 (1967)] permit an indirect evaluation in terms of the estimated overall mechanical properties or concentration factors and phase thermoelastic moduli. These two results are shown to coincide for those systems and models which return diagonally symmetric estimates of the overall stiffness. Finally, model predictions of the overall elastic symmetry of composite media are discussed with regard to the spatial distribution of the phases.

Original language | English |
---|---|

Pages (from-to) | 927-946 |

Number of pages | 20 |

Journal | Journal of the Mechanics and Physics of Solids |

Volume | 39 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1991 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Journal of the Mechanics and Physics of Solids*,

*39*(7), 927-946. https://doi.org/10.1016/0022-5096(91)90012-D

}

*Journal of the Mechanics and Physics of Solids*, vol. 39, no. 7, pp. 927-946. https://doi.org/10.1016/0022-5096(91)90012-D

**On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media.** / Benveniste, Y.; Dvorak, G. J.; Chen, Tungyang.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media

AU - Benveniste, Y.

AU - Dvorak, G. J.

AU - Chen, Tungyang

PY - 1991/1/1

Y1 - 1991/1/1

N2 - The existence of diagonal symmetry in estimates of overall stiffness tensors of heterogeneous media is examined for several micromechanical models. The dilute approximation gives symmetric estimates for all matrix-based multiphase media. The Mori-Tanaka and the self-consistent methods do so for all two-phase systems, but only for those multiphase systems where the dispersed inclusions have a similar shape and alignment. However, the differential schemes associated with the self-consistent method can predict diagonally symmetric overall stiffness and compliance for multiphase systems of arbitrary phase geometry. A related question is raised about the equivalence of two possible approaches to evaluation of the overall thermal stress and strain tensors. A direct estimate follows from each of the above models, whereas Levin's results [Mechanics of Solids 2, 58 (1967)] permit an indirect evaluation in terms of the estimated overall mechanical properties or concentration factors and phase thermoelastic moduli. These two results are shown to coincide for those systems and models which return diagonally symmetric estimates of the overall stiffness. Finally, model predictions of the overall elastic symmetry of composite media are discussed with regard to the spatial distribution of the phases.

AB - The existence of diagonal symmetry in estimates of overall stiffness tensors of heterogeneous media is examined for several micromechanical models. The dilute approximation gives symmetric estimates for all matrix-based multiphase media. The Mori-Tanaka and the self-consistent methods do so for all two-phase systems, but only for those multiphase systems where the dispersed inclusions have a similar shape and alignment. However, the differential schemes associated with the self-consistent method can predict diagonally symmetric overall stiffness and compliance for multiphase systems of arbitrary phase geometry. A related question is raised about the equivalence of two possible approaches to evaluation of the overall thermal stress and strain tensors. A direct estimate follows from each of the above models, whereas Levin's results [Mechanics of Solids 2, 58 (1967)] permit an indirect evaluation in terms of the estimated overall mechanical properties or concentration factors and phase thermoelastic moduli. These two results are shown to coincide for those systems and models which return diagonally symmetric estimates of the overall stiffness. Finally, model predictions of the overall elastic symmetry of composite media are discussed with regard to the spatial distribution of the phases.

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U2 - 10.1016/0022-5096(91)90012-D

DO - 10.1016/0022-5096(91)90012-D

M3 - Article

VL - 39

SP - 927

EP - 946

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 7

ER -