## Effective properties of composite media containing periodic arrays of spheres |

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### Contents

Effective Viscosity of a Periodic Suspension of Spheres | 14 |

Asymptotic Form of the Effective Viscosity Tensor | 39 |

Effective Viscosity Results and Discussion | 69 |

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0.60 Illustration Acrivos angular displacement arrays of spheres asymptotic analysis asymptotic expansions asymptotic form asymptotic results basis functions Body-Centered Cubic Lattices boundary conditions calculate Chapter close-packing composite material Computed and asymptotic computed results Concentration Asymptotic Formulas constitutive equations convergence cylindrical coordinate system cylindrical coordinates defined deformation gradient dependence derived deviatoric effective elasticity problem effective elasticity tensor effective property effective viscosity coefficients effective viscosity problem effective viscosity tensor evaluated face-centered cubic lattices fluid velocity four-tensor Green's identities included spheres integral equations isotropic kernel lattice of spheres Low Concentration Asymptotic moduli nearest neighbor spheres Newtonian fluid nonsingular terms numerical method numerical results obtain periodic array periodic lattice Poisson ratio pressure and fluid principal lattice sums reciprocal lattice rigid spheres shear shear modulus Simple Cubic Lattices simplify singular term solution solve sphere centered spherical stresslet integral Substituting surface force density symmetry Table tion values volume concentration yields Zuzovsky Zuzovsky's