Efficient Volume Modules of Polydispersion Composites with Spherical Inclusion

Abstract

The formula of R. M. Christensen [14], according to the definition of the volume modulus of polydisperse composites with spherical inclusion, is transformed to the dimensionless function k = k (η, θ, w) of these modules, which depends only on three dimensionless parameters. For a given value of the parameters η and θ, the modulus formula becomes a function of k = k (w) of one argument (volume fraction of inclusion). In a flat space k - w, the function k = k (w) is mapped by a curved segment between the points (0, 1) and (1, 0) of the same space. For different values of η, the function k = k (w) displays the spectrum of curved segments between the points mentioned above. This spectrum determines the position of a plane figure in the space k - w. The shape of the figure and its position (in this space) changes with other values of the parameter θ. Examples are given of constructing two similar figures for characteristic subsets of the values of the function k = k (η, θ, w).