Homogenization of an elastic medium having three phases. (English) Zbl 1320.35036

Summary: We study an elastostatic problem in an \(\epsilon\)-periodic medium having three phases: matrix, fibers, and fiber coatings. The rigidity is of order one along the fibers and is scaled by \(\epsilon^2\) (the so-called double porosity scaling) in both the transverse directions and the fiber coatings. Using the homogenization process, we show that both the effective transverse traction and the longitudinal stress in the fibers are mainly influenced by the elastic properties of the fiber coatings.


35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
74B05 Classical linear elasticity
74Q05 Homogenization in equilibrium problems of solid mechanics
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