Theory of elastic properties of composite materials

A new method of estimating effective macroscopic elastic constants for microscopically inhomogeneous materials is formulated using elastic‐wave scattering theory. The self‐consistent medium is determined by the condition that the scattered long‐wavelength displacement field must vanish on the average. The resulting formulas are simpler to apply than previous methods due to the reduction from tensor to vector equations. Our formulas are automatically symmetric under interchange of constituent labels whereas some other ’’self‐consistent’’ formulations for needle and disk inclusions do not possess this property. For spherical inclusions, the standard self‐consistent elastic constants are reproduced.

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