A mortar formulation for frictionless line-to-line beam contact

Bosten, Armin; Cosimo, Alejandro; Linn, Joachim; Bruls, Olivier

doi:10.1007/s11044-021-09799-5

Download

Article (Scientific journals)

A mortar formulation for frictionless line-to-line beam contact

Bosten, Armin; Cosimo, Alejandro; Linn, Joachim et al.

2021 • In Multibody System Dynamics

Peer reviewed

Permalink
https://hdl.handle.net/2268/262871

DOI
10.1007/s11044-021-09799-5

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

Bosten2021_Article_AMortarFormulationForFrictionl.pdf

Publisher postprint (1.44 MB)

Download

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Beam contact; Mortar; Special Euclidean group

Abstract :

[en] This paper describes the quasi-static formulation of frictionless line contact between flexible beams by employing the mortar finite element approach. Contact constraints are enforced in a weak sense along the contact region using Lagrange multipliers. A simple projection appropriate for thin beams with circular cross-sections is proposed for the computation of contact regions. It is combined with the geometrically exact beam formalism on the Lie group SE(3). Interestingly, this framework leads to a constraint gradient and a tangent stiffness invariant under rigid body transformations. The formulation is tested in some numerical examples.

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Bosten, Armin ; Université de Liège - ULiège > A&M

Cosimo, Alejandro ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire des Systèmes Multicorps et Mécatroniques

Linn, Joachim; Fraunhofer ITWM Kaiserslautern > MDF

Bruls, Olivier ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire des Systèmes Multicorps et Mécatroniques

Language :

English

Title :

A mortar formulation for frictionless line-to-line beam contact

Publication date :

25 August 2021

Journal title :

Multibody System Dynamics

ISSN :

1384-5640

eISSN :

1573-272X

Publisher :

Kluwer Academic Publishers, Netherlands

Peer reviewed :

Peer reviewed

Additional URL :

https://rdcu.be/cv7bR

Funders :

Robotix Academy project of the Greater Region
Fraunhofer Institute for Industrial Mathematics Kaiserslautern

Available on ORBi :

since 01 September 2021

Statistics

Number of views

138 (19 by ULiège)

Number of downloads

145 (16 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Sonneville, V., Cardona, A., Brüls, O.: Geometrically exact beam finite element formulated on the Special Euclidean group SE(3). Comput. Methods Appl. Mech. Eng. 268, 451–474 (2014)
Sonneville, V.: A geometric local frame approach for flexible multibody systems. PhD Thesis, University of Liège (2015)
Sonneville, V., Cardona, A., Brüls, O.: Geometric interpretation of a non-linear finite element on the Lie group SE(3). Arch. Mech. Eng. 61, 305–329 (2014)
Borri, M., Botasso, C.: An intrinsic beam model based on a helicoidal approximation. Int. J. Numer. Methods Eng. 37, 2267–2289 (1994)
Kirchhoff, G.: Über das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes. J. Reine Angew. Math. 56, 285–313 (1859)
Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity, 4th edn. Cambridge University Press, UK (1927)
Reissner, E.: On one-dimensional large-displacement finite-strain beam theory. Stud. Appl. Math. 2, 87–95 (1973)
Simo, J.C.: A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Comput. Methods Appl. Mech. Eng. 49, 55–70 (1985)
Belgacem, F.B.: The Mortar finite element method with Lagrange multipliers. Numer. Math. 84, 173–197 (1999)
Wohlmuth, B.: Variationally consistent discretization schemes and numerical algorithms for contact problems. Acta Numer. 20, 569–734 (2011)
Belgacem, F.B., Renard, Y.: Hybrid finite element methods for the Signorini problem. Math. Comput. 72, 1117–1145 (2003)
Popp, A.: Mortar methods for computational contact mechanics and general interface problems. PhD Thesis, Teschnische Universität München (2012)
Cavalieri, F.J., Cardona, A.: An augmented Lagrangian technique combined with a mortar algorithm for modeling mechanical contact problems. Int. J. Numer. Methods Eng. 93(4), 420–442 (2012)
Alart, P., Curnier, A.: A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput. Methods Appl. Mech. Eng. 92, 353–375 (1990)
Lolić, D., Zupan, D., Brojan, M.: A consistent strain-based beam element with quaternion representation of rotations. Comput. Mech. 65, 1397–1412 (2020)
Brüls, O., Cardona, A., Arnold, M.: Lie group generalized- α time integration of constrained flexible multibody systems. Mech. Mach. Theory 48, 121–138 (2012)
Meier, C., Popp, A., Wall, W.A.: A finite element approach for the line-to-line contact interaction of thin beams with arbitrary orientation. Comput. Methods Appl. Mech. Eng. 308, 377–413 (2016)
Denoël, V.: Advantages of a semi-analytical approach for the analysis of an evolving structure with contacts. Commun. Numer. Methods Eng. 0, 1–6 (2002)
Meier, C., Popp, A., Wall, W.A.: A locking-free finite element formulation and reduced models for geometrically exact Kirchhoff rods. Comput. Methods Appl. Mech. Eng. 290, 314–341 (2015)
Meier, C., Popp, A., Wall, W.A.: An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods. Comput. Methods Appl. Mech. Eng. 278, 445–478 (2014)
Meier, C., Wall, W.A., Popp, A.: Geometrically exact finite element formulations for curved slender beams: Kirchhoff-Love theory vs. Simo–Reissner theory. Arch. Comput. Methods Eng. 26, 163–243 (2019)
Audoly, B., Pomeau, Y.: Elasticity and Geometry—From Hair Curls to the Non-linear Response of Shells. Oxford University Press, Oxford, UK (2006)
Bertails, F., Audoly, B., Cani, M., Querleux, B., Leroy, F., Lévêque, J.: Super-Helices for Predicting the Dynamics of Natural Hair. In: Proceedings of the ACM SIGGRAPH (2006)
Jelenić, G., Crisfield, M.A.: Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics. Comput. Methods Appl. Mech. Eng. 171, 141–171 (1999)
Crisfield, M.A., Jelenić, G.: Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation. Proc. R. Soc. Lond. A 455, 1125–1147 (1999)
Cardona, A., Géradin, M.: A beam finite element non-linear theory with finite rotations. Int. J. Numer. Methods Eng. 26, 2403–2438 (1988)
Cottanceau, E., Thomas, O., Véron, P., Alochet, M., Deligny, R.: A finite element/quaternion/asymptotic numerical method for the 3 D simulation of flexible cables. Finite Elem. Anal. Des. 139, 14–34 (2018)
Grazioso, S., Di Gironimo, G., Siciliano, B.: A geometrically exact model for soft continuum robots: the finite element deformation space formulation. Soft Robot. 6, 790–911 (2019)
Jödicke, R., Jungnickel, U., Müller, A.: Lie group modeling of nonlinear helical beam elements. In: Proceedings of the ASME IDETC/CIE (2014)
Sonneville, V., Brüls, O., Bauchau, O.: Interpolation schemes for geometrically exact beams: a motion approach. Int. J. Numer. Methods Eng. 112, 1129–1153 (2017)
Kikuchi, N., Oden, J.T.: Contact Problems in Elasticity. SIAM Studies in Applied and Numerical Mathematics (1988)
Laursen, T.A.: Computational Contact and Impact Mechanics. Springer, Berlin (2003)
Wriggers, P., Zavarise, G.: On contact between three-dimensional beams undergoing large deflections. Commun. Numer. Methods Eng. 13, 42–438 (1997)
Zavarise, G., Wriggers, P.: Contact with friction between beams in 3-D space. Int. J. Numer. Methods Eng. 49, 977–1006 (2000)
Chamekh, M., Mani-Aouadi, S., Moakher, M.: Modeling and numerical treatment of elastic rods with frictionless self-contact. Comput. Methods Appl. Mech. Eng. 198, 3751–3764 (2009)
Meier, C., Grill, M.J., Wall, W.A., Popp, A.: Geometrically exact beam elements and smooth contact schemes for the modeling of fiber-based materials and structures. Int. J. Solids Struct. 154, 124–146 (2018)
Durville, D.: Contact-friction modeling within elastic beam assemblies: an application to knot tightening. Comput. Mech. 49, 687–707 (2012)
Durville, D.: Numerical simulation of entangled materials mechanical properties. J. Mater. Sci. 40, 5941–5948 (2005)
Bertails, F., Cadoux, F., Daviet, G., Acary, V.: A nonsmooth Newton solver for capturing exact Coulomb friction in fiber assemblies. ACM Trans. Graph. 30, 1–14 (2011)
Hueber, S., Wohlmuth, B.: A primal–dual active set strategy for non-linear multibody contact problems. Comput. Methods Appl. Mech. Eng. 194, 3147–3166 (2005)
Farah, P., Wall, W.A.: A mortar finite element approach for point, line and surface contact. Int. J. Numer. Methods Eng. 00, 1–44 (2017)
Gitterle, M., Popp, A., Gee, M.W., Wall, W.A.: Finite deformation frictional mortar contact using a semi-smooth Newton method with consistent linearization. Int. J. Numer. Methods Eng. 84, 543–571 (2010)
Popp, A., Wall, W.A.: Dual mortar methods for computational contact mechanics – overview and recent developments. GAMM-Mitt. 37(1), 66–84 (2014)
Puso, M.A., Laursen, T.A.: A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. Eng. 193, 601–629 (2004)
Raviart, P.A., Thomas, J.M.: Primal hybrid finite element methods for 2nd order elliptic equations. Math. Comput. 31, 391–413 (1977)
Yang, B., Laursen, T.A., Meng, X.: Two dimensional mortar contact methods for large deformation frictional sliding. Int. J. Numer. Methods Eng. 62, 1183–1225 (2005)
Han, S., Bauchau, O.: On the global interpolation of motion. Comput. Methods Appl. Mech. Eng. 337, 352–386 (2018)
Bauchau, O., Han, S.: Interpolation of rotation and motion. Multibody Syst. Dyn. 31, 339–370 (2014)
Chen, J-S.: On the contact behavior of a buckled Timoshenko beam constrained laterally by a plane wall. Acta Mech. 222, 225–232 (2011)
Odin: a research code for the simulation of nonsmooth flexible multibody systems. University of Liège, Department of Aerospace and Mechanical Engineering. To be released as opensource under the Apache v2 license
Arnold, M., Brüls, O., Linn, J.: THREAD-numerical modeling of highly flexible structures for industrial applications. In: Celledoni, E., Münch, A. (eds.) Mathematics with industry: driving innovation-ECMI Annual Report 2019, pp. 20–25 (2019)