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

• Applicants: Professor Dr. Alexander Konyukhov; Professor Dr.-Ing. Karl Schweizerhof
• Subject Area: Mechanics ; Theoretical Chemistry: Molecules, Materials, Surfaces
• Term: from 2013 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 233359244

• Final Report Year: 2019

Final Report Abstract

During working time of the project the following planned goals have been achieved. The family of solid-beam finite elements based on the 3D description of the continuum has been developed. This family is characterized by the elliptical cross-section and the isogeometric parametrization of the mid-line. This allows to model cable, wire and curvilinear beam-like structures as a 3D continuum possessing the necessary material law and preserving the exact C1-continuous geometry of those structures. Due to the enhanced assumed strain (EAS) technique, these solidbeam finite elements have been developed as locking free and no kinematics have been observed in all specific investigations. A special Curve-To-Solid Beam (CTSB) contact formulation has been developed in order to describe the contact between solid-beam finite elements. This formulation is strictly based on the result for existence and uniqueness of the corresponding closest Point Projection (CPP) procedure. Altogether solid-beam finite elements and corresponding contact algorithm are fully applicable to the case with “parallel tangents” of contacting curves, which is a standard case for wire ropes. A special numerical contact algorithm for modeling of ropes on the rigid surfaces has been developed. This result allows to avoid the meshing of the rigid surfaces taking the direct CAD geometry instead. The Nitsche method to enforce the contact conditions has been studied along with the standard approaches such as penalty, Lagrange multipliers and augmented Lagrangian methods. The implemented numerical integration technique with subdivisions allows to describe the contact line with a prescribed tolerance. In addition, the algorithm for follower forces arising from contact and possessing the symmetry of corresponding tangent matrices has been developed. This algorithm allows to effectively apply both bending and torsional moments, which are typical in conventional beam theories, to the solid-beam finite elements. As deviations from the project the following novel results in contact mechanics have been achieved: 1. Generalization of the Euler-Eytelwein formula for ropes with friction on orthotropic surfaces of arbitrary geometry. This result is the generalization of the famous Euler result from 1769 and popularized in Eytelwein’s book from 1808 and can be directly taken into standard courses of Technical Mechanics taught in German Universities. 2. New contact algorithms for the finite cell method (FCM). Several contact algorithms have been developed. These algorithms are varying based on the priority for the research goals: the fastest implementation or the highest tolerance. Achieved results are directly applicable for wire ropes modeling as well as have a big potential for further developments of models for composite wire ropes and cables.

Publications

• A Six-Node Solid-Beam Finite Element with Elliptic Cross Section, 84th Annual Meeting of Gesellschaft für Angewandte Mathematik und Mechanik, GAMM 2013, Novi Sad, Serbia, 18-22 March, 2013
  Strobl M., Konyukhov A., Schweizerhof K.
  
• A solid beam element for wire rope simulation with a special contact algorithm. 11th World Congress on Computational Mechanics (WCCM XI), 20-25 July 2014, Barcelona, Spain
  Schweizerhof K., Konyukhov A., Izi R. and Strobl M.
  (See online at https://doi.org/10.13140/2.1.1100.7369)
• Geometrically exact theory of contact interactions – a general approach with a special focus on curve-to-surface contact. GAMM-Mitteilungen, Wiley-VCH, 37 (1), 7-26
  Konyukhov A., Schweizerhof K.
  (See online at https://doi.org/10.1002/gamm.201410002)
• Contact of ropes and orthotropic rough surfaces. ZAMM, Wiley-VCH, 95 (4), 406-423, 2015
  Konyukhov A.
  (See online at https://doi.org/10.1002/zamm.201300129)
• Introduction into Computational Contact Mechanics – Geometrical Approach. Wiley, 304 p. 2015
  Konyukhov A., Izi R.
  
• On some aspects for contact with rigid surfaces: surfaceto-rigid surface and curve-to-rigid surface algorithms, Computer Methods in Applied Mechanics and Engineering, 2015, 283, 74-105
  Konyukhov A., Schweizerhof K.
  (See online at https://doi.org/10.1016/j.cma.2014.08.013)
• Various contact approaches for the Finite Cell Method, Computational Mechanics, 56:331?351
  Konyukhov A., Ch. Lorenz, Schweizerhof K.
  (See online at https://doi.org/10.1007/s00466-015-1174-x)
• General descriptions of follower forces derived via a geometrically exact inverse contact algorithm. International Journal for Numerical Methods in Engineering, Vol. 108 (11): 1290 – 1306, 2016
  Konyukhov A.
  (See online at https://doi.org/10.1002/nme.5253)
• An interface finite element based on a frictional contact formulation with an associative plasticity model for the tangential interaction. International Journal for Numerical Methods in Engineering, Vol. 111 (8), 2017, 753–775
  Michaloudis G., Konyukhov A., Gebbeken N.
  (See online at https://doi.org/10.1002/nme.5485)
• Consistent Development of a Beam-To-Beam Contact Algorithm via the Curve to Solid Beam Contact - Analysis for the Non-Frictional Case, International Journal for Numerical Methods in Engineering. Vol. 113 (7), 2018, 1108-1144
  Konyukhov A., Mrenes O., Schweizerhof K.
  (See online at https://doi.org/10.1002/nme.5701)