Textiles are discrete and highly inhomogeneous materials, which makes their modelling difficult. Models of three different kinds have emerged throughout the literature: geometrical models [PEIRCE (1937)], mechanical or force models [PEIRCE (1937), OLOFSSON (1964)] and energetic models [DE JONG and POSTLE (1977and 1978)]. Three main scales can be identified: the microscopic scale (the yarn), the macroscopic scale and the intermediate scale (the undulation of the yarn), called here and in the sequel the mesoscopic scale. Studying the behavior of the thread is an essential step towards the analysis at the mesoscopic and the macroscopic scales. A geometric homogenization technique is first applied in order to obtain a limit model of a straight beam. Equivalent mechanical moduli are obtained, which in turn allow to draw "traction curves". Next, a constitutive law in large transformations is given, through a micropolar hyperelastic constitutive law.
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