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Computational homogenization of rope-like technical textiles. (English) Zbl 1311.74100

Summary: This contribution investigates a computational homogenization method for one-dimensional technical textiles i.e. ropes or cables. On the macroscopic level rope-like textiles are characterized by a large length-to-thickness ratio, such that a discretization with structural elements, i.e. beam elements, is numerically efficient. The material behavior is, however, strongly influenced by the heterogeneous micro structure. Here, the fibers at the micro structure are modeled explicitly via a representative volume element whereby the contact interactions between fibers are captured. To transfer the microscopic response to the macro level a beam specific homogenization scheme is introduced. Theoretical aspects are discussed, e.g. the advocated beam specific power averaging theorem and the corresponding scale transition, and numerical examples for periodic rope-like structures are given.

MSC:

74Q05 Homogenization in equilibrium problems of solid mechanics
74K05 Strings
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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