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Linear theory of disordered fibre-reinforced composites. (English) Zbl 0554.73002

Each fibre with random position and orientation is treated as embedded in an effective, i.e. averaged medium. Contribution of each fibre to the total effective Green function, the main goal of the paper, is then determined in a self-consistent manner. Neglection of the fluctuations about the averaged fibre environment renders a sufficiently good approximation in the limits of low and high concentrations of those straight fibres. Effects of distribution of fibre lengths and non-zero frequency (by modal expansion) are discussed only very briefly. Shear stress at the fibre-matrix interface is determined explicitly. A theory of rigid random walks in an incompressible matrix shows limits when local details of the single fibre are no more relevant. Theory is related to the ”dishonest” method of Karal and Keller. It should improve the engineering formulations of Haskin and others, not given any reference in the paper.
Reviewer: F.Ziegler

MSC:

74A40 Random materials and composite materials
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
74J20 Wave scattering in solid mechanics
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