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Strong-contrast expansion correlation approximations for the effective elastic moduli of multiphase composites. (English) Zbl 1293.74362

Summary: Following the previous approach of D. C. Pham and S. Torquato [“Strong-contrast expansions and approximations for the effective conductivity of isotropic multi-phase composites”, J. Appl. Phys. 94, 6591–6602 (2003)] and S. Torquato [J. Mech. Phys. Solids 45, No. 9, 1421–1448 (1997; Zbl 0974.74553); Random heterogeneous media. Berlin: Springer (2002)], we derive the strong-contrast expansions for the effective elastic moduli \(K_{\mathrm e}\), \(G_{\mathrm e}\) of \(d\)-dimensional multiphase composites. The series consists of a principal reference part and a fluctuation part (perturbation about a homogeneous reference or comparison material), which contains multi-point correlation functions that characterize the microstructure of the composite. We propose a three-point correlation approximation for the fluctuation part with an objective choice of the reference phase moduli, such that the fluctuation terms vanish. That results in the approximations for the effective elastic moduli of isotropic composites, which coincide with the well-known self-consistent and Maxwell approximations for two-phase composites having respective microstructures. Applications to some two-phase materials are given.

MSC:

74Q15 Effective constitutive equations in solid mechanics
74E30 Composite and mixture properties

Citations:

Zbl 0974.74553
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References:

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