Dispersion-stiffened composite

Verify that the general expression for the nxxfulus of a dispersion-stiffened composite material reduces to... 

Consider a dispersion-stiffened composite material. Determine the Influence on the upper bound for the apparent Young s modulus of different Poisson s ratios in the matrix and In the dispersed material. Consider the following three combinations of material properties of the constituent materials ... 

Use the bounding techniques of elasticity to determine upper and lower bounds on the shear modulus, G, of a dispersion-stiffened composite materietl. Express the results In terms of the shear moduli of the constituents (G for the matrix and G for the dispersed particles) and their respective volume fractions (V and V,j). The representative volume element of the composite material should be subjected to a macroscopically uniform shear stress t which results in a macroscopically uniform shear strain y. 

Determine the bounds on E for a dispersion-stiffened composite material of more than two constituents, i.e., more than one type of particle is dispersed in a matrix material. 

In general, the following principle is used in the incorporation of dispersed phase into the matrix, in the production of a composite the matrices selected for use are of lower modulus, while the dispersed reinforcing elements are typically some 50 times stronger and 20-150 times stiffen One should note, that the properties of the matrix are particularly important in most polymer composite systems - as in such systems, the matrix bears the load and it is distributed between the matrix and reinforcing particles. Each matrix type with different incorporated phases certainly has a different impact on the processing technique to be used. 

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