Static elastic and thermoelastic field fluctuations in multiphase composites.

*(English)*Zbl 0601.73001The spatially fluctuating strain and stress fields in a random heterogeneous thermoelastic medium are characterized by their mean values and square means in each phase. In the present paper the calculation of these quantities, which has been presented in a previous work for the case of a mechanical load only [the authors, ibid. 34, 1-18 (1986)] is extended to include thermal expansion. Besides the derivation of some exact relations between the square means and the analytical properties of the effective thermal expansion coefficient the field fluctuations are calculated within an effective-medium procedure supposing an aggregate topology of the composite. Explicit results obtained for isotropic phases and spherical grain shapes are given in a more convenient representation than in our former work.

##### MSC:

74F05 | Thermal effects in solid mechanics |

74A40 | Random materials and composite materials |

74E05 | Inhomogeneity in solid mechanics |

74A60 | Micromechanical theories |

74M25 | Micromechanics of solids |

##### Keywords:

self-consistent single-grain approximation; spatially fluctuating strain; stress fields; random heterogeneous thermoelastic medium; mean values; square means; thermal expansion
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\textit{M. Bobeth} and \textit{G. Diener}, J. Mech. Phys. Solids 35, 137--149 (1987; Zbl 0601.73001)

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