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

钢丝绳、复合钢丝绳和纤维束及其技术应用提出了非常重要的实际问题以及计算上具有挑战性的问题，这些问题大多是最新未解决的，特别是在细节方面。只有一些近似的公式是可用的，但问题，如滑动和摩擦的单独部分和与其他机构以及横截面变形-重要的失败，这种结构的断裂和耐久性-复合材料钢丝绳和缆索的机械相互作用除了考虑单根钢丝的力学外，还需要为各种运动学情况建立接触模型，如绞合和绞合的金属丝、金属丝股和复合金属丝绳、纤维束和结以及织物。“曲线到曲线”接触方法允许描述变形的完整相对运动学，并提供了创建钢丝绳的精确和非简化模型的很大可能性，该模型也可用于复合绳的均匀化。一种特殊的有限梁单元模型，其富含允许$C1$-连续性的等几何技术，并将被开发为绳和钢丝的基本模型。作为一个重要的和有效的替代曲线“固体梁”元素也允许C1 $-连续性和各种各向异性将创建。结和复合绳内的接触相互作用将丰富的各向异性摩擦的可能性，不仅包括经典的切向相互作用，但扭转相互作用分别为每个曲线。用“任意曲面上的曲线绳索”的描述丰富了绳索与表面之间的接触相互作用。 将创建具有精确运动学的复合钢丝绳的精确模型（分离的钢丝是可变形的并且是接触的）。所开发的有限元模型肯定会改善结力学，并允许正确描述复合钢丝绳的行为，以及正确模拟纤维、纤维束和完整纺织品之间的纺织品连接-这是迄今为止计算上尚未解决的问题。

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.