Abstract
We describe a new, effective medium theory to study the wave propagation and mechanical properties of a composite system with dispersed particulates. One main emphasis here is in formulating the theory and in analyzing the structure of the contribution of the fillers to the elastic response. By constructing the elastic propagator (whose fluid mechanical counterpart is known as the Oseen tensor), we show that an analogy between the theoretical description of the particulate system and of suspension rheology exists when the former corresponds to a high-rigidity solid matrix (or, analogously, when the Poisson ratio is close to 1/2) in steady state. The effective Lamé constants for this case are derived by combining this analogy with the theory developed by Freed and Muthukumar for the rheology of a suspension of spheres. The analogy is also useful in our new prediction of the phenomenon of elastic screening, the possible existence of a cutoff frequency below which elastic waves cannot propagate in the filler system.
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Research supported by ALCOA and MRL (NSF) facilities at The University of Chicago.
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Jhon, M.S., Metz, R.J. & Freed, K.F. Effective medium theory for elastic matrix composites containing dispersed particulates. J Stat Phys 52, 1325–1342 (1988). https://doi.org/10.1007/BF01011650
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DOI: https://doi.org/10.1007/BF01011650