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Effective properties of elastic periodic composite media with fibers. (English) Zbl 1170.74042
Summary: We derive a series solution to obtain the effective properties of some elastic composites media having periodically located heterogeneities. The method uses the classical Neumann series for the solution of the periodic elasticity problem in Fourier space, based on the Green’s tensor, and exact expressions of factors depending on the shape of the inclusions. Some properties of convergence of the solution are presented, more specifically concerning the elasticity tensor of the reference medium, showing that the convergence occurs even for empty fibers. The solution is extended to rigid inclusions. A comparison is made with previous exact solutions for a fiber composite made of cylindrical fibers with circular cross-sections and with previous estimates. Different examples are presented for new situations concerning the study of fiber composites: composites with elliptic cross-sections and multi-phase fibrous composites.

MSC:
74Q15 Effective constitutive equations in solid mechanics
74Q05 Homogenization in equilibrium problems of solid mechanics
74E30 Composite and mixture properties
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