Bounds and expressions for the elastic moduli of two or many phase nonhomogeneous materials are obtained by an approximate method based on the variational theorems of the theory of elasticity and on a concentric-spheres model. Theoretical results are in good agreement with experimental results for a two-phase alloy.
The Elastic Moduli of Heterogeneous Materials
The Towne School of Civil and Mechanical Engineering, University of Pennsylvania, Philadelphia, Pa.
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Hashin, Z. (March 1, 1962). "The Elastic Moduli of Heterogeneous Materials." ASME. J. Appl. Mech. March 1962; 29(1): 143–150. https://doi.org/10.1115/1.3636446
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