High-order accurate calculations and bounds on effective properties of composites

Sammanfattning: A classical problem in material science has been the studyof electrostatic and elastostatic properties of compositematerials. The complexity of the microstructure of randomcomposite media makes an exact calculation of the effectiveproperties very difficult. This naturally leads to the attemptto estimate the properties from partial structural information.Considerable theoretical progress has been made in the lastdecade on the derivation of bounds. There has been relativelyless research directed towards solving the governing equationsaccurately. Such calculations could provide tests on theoriesfor well-defined model microstructures.This thesis considers high-order accurate calculations andbounds on some physical properties of composites. Specialattention is paid to the calculation of structural parametersthat enter certain parameter-dependent bounds. The high-orderaccurate calculations on some non-trivial microstructures areperformed with interface integral equation methods. Thecomposites are allowed to have anisotropic componentproperties.The main results in the thesis are:    Estimates of the thermal and electrical conductivity ofcementite (Fe3C) over a wide range of temperatures.    Expressions for the structural parameters ζ2and η2for a class of fiber-reinforced composites.    Numerical calculations of the above mentioned parametersfor hundreds of millions of structures. to obtain realizableregions in the ζ2- η2plane.    Highly accurate numerical calculations of the effectivePoisson's ratio for some fiber-reinforced composites. Aformulation of a general statement for Poisson's ratio flowdiagrams.    Highly accurate numerical calculations of the effectiveconductivity tensor for composite films in an appliedperpendicular magnetic field. Asymptotic studies of theeffective Hall conductivity in these systems.Keywords:electrostatic and elastostatic properties ofcomposites, parameterdependent bounds, effective Poisson'sratio, interface integral equations, effective Hallconductivity tensor