In various applications, it is common to use thin beam-like structures, made of plastic or fibre-reinforced materials, as well as components such as cables. They are flexible, and the most common form of deformation is bending, but they can also be stretched or torqued. Due to their structural composition, a coupling between the different loading directions exists. This is especially pronounced for cables, where the different components interact with each other and the kinematics of each component are different. Thus, to characterise these materials, it is necessary to consider tension, torsion, bending, and a coupling of the three load cases. In this work, such characterisations are performed for a polyvinyl chloride rod, a carbon fibre-reinforced rod, and a coaxial cable. The three materials represent the isotropic and anisotropic material classes and include homogeneous and non-homogeneous cross-sections. An anisotropic elasto-plastic material model is implemented in the finite element method to model the behaviour of such structures. The material model includes anisotropic plasticity so that the structural effects can also be modelled for large deformations. Thin structures are discretised with higher-order elements, and a comparison of the experimental and the simulation results is presented.

In this paper, a hierarchic high-order three-dimensional finite element formulation is studied for hyperelastic and anisotropic elastoplastic problems at finite strains. The element formulation allows for anisotropic ansatz spaces supporting efficient discretizations of beam-, plate-, and shell-like structures. Several benchmark examples are investigated and the results of the high-order formulation are compared to analytic solutions and different mixed finite element formulations. Special emphasis will be placed on locking effects, robustness with respect to high aspect ratios and element distortion as well as anisotropies related to the material model. Furthermore, the interplay between the chosen ansatz space for the displacement field and mapping function in the context of geometrically nonlinear problems are studied.

Cables are slender structures with a complex geometry, that can undergo large deformations during their installation or in dynamic environments. In combination with their complex inner structure they pose a challenging problem for finite element simulations. In this article a simplified approach is presented to model cables by using an effective material and a homogeneous cross-section, which is anisotropic in the elastic and inelastic domain. For the high-order hierarchic shape functions with quasi-regional mapping, anisotropic ansatz spaces are applied in tension, torsion and bending simulations. The identification of material parameters is conducted based on experimental results for a tension and a torsion test using the particle swarm optimization algorithm. Finally, the identified parameters are validated for a combined load case with torsion and free bending, showing a promising approach regarding the simulation of cable structures.

The mechanical characterisation of cables can help improving the production and lifetime of various products, for example a robotic arm. Cables however form a class of composite structures, that is highly anisotropic and dissipates energy due to the reorientation of its constituents which is superimposed by the dissipation due to the deformation of the polymer components. Cables also have a degree of randomness in their structure. Moreover, the stiffness in one loading direction is coupled to the stiffness in another loading direction.In this work, experimental investigations on the mechanical properties of the cables are presented. An experimental setup has been constructed to test the cables in tensile, torsion and the bending directions individually as well as coupled to each other. Free bending tests were conducted where axial forces were compensated during the bending to dissociate the tensile and the bending properties of the cables. To apply larger tensile and torsional loads on cables a commercial testing device was also used. To characterise the influence of bending on torsion, free bending tests were conducted with a combination of torsional load. Thus, a complete mechanical characterisation of a cable is presented.

Due to their complex structure cables exhibit an anisotropic behaviour and undergo large deformations in various applications. The large deformations are simulated using blended high order solid elements that can represent large deformations efficiently. To reduce the computational complexity the cross section consisting of many single wires and different layers of material is homogenized and represented by a transversely isotropic material model. Frictional effects and possible reordering of the parts are modelled through elastoplastic material behaviour with an anisotropic yield function. The simulations show that for a simple tension test and a free torsion test the material parameters can be satisfactorily identified.