Modelling and simulation of cables with high-order finite elements

Project Leader:

Prof. Dr.-Ing. habil. Alexander Düster

Project members:

André Hildebrandt

Project partners:

M.Sc. Prateek Sharma (UdS), Prof. Dr.-Ing. Stefan Diebels (UdS)

Funding party:

DFG (German Research Foundation)

Duration:

02.2019- 01.2021

Introduction:

Cables are an ubiquitous part of the modern world. In engineering applications for instance they serve as structural elements in bridges and ski lifts, feed lines in maritime applications, electrical conductors, or as a medium for signal transmission. Many applications like signal-cables in robotics lead to large displacements combined with small strains. Additionally, during installation cables can get pulled over edges which can lead to high local deformations due to contact. In [1] experiments on a coaxial cable under different loading situations have been conducted, stating that realistic loading situations are mostly multiaxial and combine several basic load cases as tension, torsion, and bending. Electric cables consist of different materials such as a conductive core, an insulation of the wires, and a rubber coating. Sometimes additional reinforcing or screening layers of glass fibre are added. The mechanical behaviour can be considered as hypereleastic, elastoplasctic, or viscoplastic. Further dissipation is introduced by friction, rupture, geometrical effects, or reordering of the parts.

For the structural analysis this project uses the high-order FEM with anisotropic hexahedral elements, which enables efficient modelling due to the possibility of using different polynomial orders for the individual directions [2]. Additionally, it is expected that locking-phenomena can be overcome through p-refinement.

References:

[1] Dörlich, V., Linn, J., Scheer, T., & Diebels, S., 2016. Towards viscoplastic constitutive models for Cosserat rods. Archive of Mechanical Engineering, 63(2), 215-230.
[2] Düster, A., Broker, H. & Rank., E., 2001. The p-version of the finite element method for three-dimensional curved thin walled structures. International Journal for Numerical Methods in Engineering, 52(7), 673-703.
[3] Drücker, S., 2016. Elastoplastic simulation of cables using high-order finite elements. Project work, Institut für Konstruktion und Festigkeit von Schiffen, Hamburg University of Technology, Germany.
[4] de Souza Neto, E. A., Peric, D., & Owen, D. R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons, ISBN: 978-0-470-69452-7.
[5] Taghipour, A., Parvizian, J., Heinze, S., Düster, A., 2018. The finite cell method for nearly incompressible nite strain plasticity problems with complex geometries. Computers & Mathematics with Applications, 75(9), 3298-3316.
[6] Sansour, C., Karsaj, I., & Soric, J., 2006. A formulation of anisotropic continuum elastoplasticity at finite strains. Part I: Modelling. International journal of plasticity, 22(12), 2346-2365.