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Non-local effective relations for fibre-reinforced composites loaded by configuration-dependent body forces. (English) Zbl 0991.74009

Summary: We analyze fibre-reinforced media. The distribution of the fibres is assumed random, and a combination of deterministic and configuration-dependent body forces is considered. In this case, several non-local effective constitutive operators must be taken into account in order to define the mean response of the material. For two-phase composites, we obtain expressions for all these operators, and in the case of fibre-reinforced materials we derive explicit Hashin-Shtrikman type bounds in the real and Fourier spaces. Finally, a periodic distribution of fibres is studied as an example.

MSC:

74A40 Random materials and composite materials
74Q20 Bounds on effective properties in solid mechanics
74E30 Composite and mixture properties
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