Mechanical models for twisted cables and wire ropes involving complex contact interaction between fibers and their parts: mechanics of knots, splices and nets.

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Wire strands, composite wire ropes and fiber bundles and their technical applications are posing very important practical problems as well as computationally challenging issues, which are mostly up to date unsolved, particularly also in the details. Only somehow approximate formulas are available, but problems as sliding and friction of separate parts and with other bodies as well as the cross-sectional deformation – important for the failure, fracture and durability of such structures – still remain open.Mechanical interactions for composite wire ropes and cables require besides consideration of mechanics for a single wire also the development of contact models for various kinematical situations such as twisted and intersected wires, wire strands and composite wire ropes, fiber bundles and knots as well as fabrics. The “curve-to-curve”' contact approach allows to describe the full relative kinematics of deformations and gives the large possibility to create exact and not simplified models of wire ropes, which can be used also for homogenization in case of composite ropes.A special finite beam element model enriched with an isogeometric technique allowing $C1$-continuity and will be developed as a basic model of ropes and wires. As an essential and efficient alternative a curvilinear “solid-beam” element also allowing $C1$-continuity and various anisotropies will be created. The contact interaction inside knots and composite ropes will be enriched with the possibility of anisotropic friction including not only classical tangential interaction, but also torsional interaction separately for each curve. The contact interaction between ropes and surfaces will be enriched with a description of “curvilinear rope on an arbitrary curvilinear surface”. An exact model of a composite wire rope with precise kinematics (a separated wire is deformable and is in contact) will be created. The developed finite element models will definitely improve the knot mechanics and allow the correct description of the behavior of the composite wire rope as well as the correct contact simulation of textile connections by fibres, fiber bundles and complete textiles – an up-to-now computationally unsolved problem.