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The Clausius-Mossotti formula in a dilute random medium with fixed volume fraction. (English) Zbl 1326.74111

A random medium with dispersed spherical identical inclusions embedded in a bounded domain is considered. The number of inclusions tends to infinity but their volume fraction remains fixed. A boundary value problem for the Laplace equation for the considered perforated domain is stated and the convergence of its solution in a Sobolev space to the solution of the homogenized problem is investigated for sufficiently small volume fractions. The result yields the Clausius-Mossotti formula. This improves a previous result presented in the paper [J. S. Choi and J. Yoo, Comput. Methods Appl. Mech. Eng. 198, No. 27–29, 2111–2121 (2009; Zbl 1227.78027)].

MSC:

74Q15 Effective constitutive equations in solid mechanics
74E35 Random structure in solid mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35R60 PDEs with randomness, stochastic partial differential equations
60K37 Processes in random environments
74Q20 Bounds on effective properties in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids

Citations:

Zbl 1227.78027
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References:

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