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Two-dimensional models of fabrics. (Modèles bidimensionnels de tissés.) (French. Abridged English version) Zbl 0793.73062

Summary: We study different models, heterogeneous or homogenized, of a fabric where shearing between warp and weft is taken into account. To this aim, we introduce two two-dimensional displacement fields in the areas where warp and weft are superposed. If warp and weft interact through elastic forces, a classical study of functional analysis shows that the problem has unique solution. The homogenization method for periodic media applied to this model of fabric yields different macroscopic models describing the strength of the coupling between warp and weft and whether the fabric is coated or not.

MSC:

74E30 Composite and mixture properties
74E05 Inhomogeneity in solid mechanics
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