Consolidated bibliography of the contact chapter and the related appendices of the PhD thesis behind the application, with the key references on mortar methods, augmented Lagrangian contact, search algorithms, automatic differentiation and constrained optimisation.
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Sources. The “Bibliography of chapter” sections of the thesis: Chapter 4 (pp. 179–188), Appendix A (p. 292), Appendix C (p. 310), Appendix D (p. 336) and Appendix E (p. 346). Keys in brackets are the citation keys used in the thesis text and reproduced in the theory pages of this documentation (e.g. “[PhDPop12]”). DOIs are linked where the thesis provides them.

Key references

The formulation implemented in the application rests mainly on the following works (the thesis section that uses each is indicated):

| Key | Reference | Used for | |—|—|—|

[PhDPop12] “Mortar Methods for Computational Contact Mechanics and General Interface Problems”. Alexander Popp. 2012. dual mortar contact, consistent linearisation, static condensation (thesis §4.3, §4.6)
[ArtPop+10] “A dual mortar approach for 3D finite deformation contact with consistent linearization”. Alexander Popp, Markus Gitterle, Michael W. Gee, and Wolfgang A. Wall. In: International Journal for Numerical Methods in Engineering. No. 11, Vol. 83, 2010, pp. 1428–1465. John Wiley & Sons, Ltd. DOI: 10.1002/nme.2866. 3D dual mortar contact with consistent linearisation (§4.3.3.4)
[BookWoh01] Discretization Methods and Iterative Solvers Based on Domain Decomposition. Barbara I. Wohlmuth. Springer-Verlag Berlin Heidelberg. 1st ed. 2001. dual Lagrange multipliers, mortar domain decomposition (§4.3.3.4.1, App. A.3)
[ArtWoh02] “A Comparison of Dual Lagrange Multiplier Spaces for Mortar Finite Element Discretizations”. Barbara I. Wohlmuth. In: ESAIM: Mathematical Modelling and Numerical Analysis. No. 6, Vol. 36, 2002, pp. 995–1012. EDP Sciences. DOI: 10.1051/m2an:2003002. biorthogonal dual basis (§4.3.3.4.1)
[ArtAC91] “A mixed formulation for frictional contact problems prone to Newton like solution methods”. P. Alart and A. Curnier. In: Computer Methods in Applied Mechanics and Engineering. No. 3, Vol. 92, 1991, pp. 353–375. DOI: 10.1016/0045-7825(91)90022-X. augmented Lagrangian for frictional contact, Newton-like solution (§4.3.3.2.1.3, §4.3.4)
[ArtBMP] “The adapted augmented Lagrangian method: a new method for the resolution of the mechanical frictional contact problem”. Philippe Bussetta, Daniel Marceau, and Jean-Philippe Ponthot. In: Computational Mechanics. No. 2, , pp. 259–275. DOI: 10.1007/s00466-011-0644-z. adapted augmented Lagrangian method, penalty adaptation (App. D.4.3.1, AALMAdaptPenaltyValueProcess)
[ArtCC12] “An augumented lagrangian method to solve three-dimensional nonlinear contact problems”. FJ Calavalieri and Alberto Cardona. In: Latin American applied research. No. 3, Vol. 42, 2012, pp. 281–289. SciELO Argentina. ALM parameter calibration ε = k ≈ 10 E/h (§4.3.3.2.1.3, §4.3.3.3)
[ArtCC13b] “An augmented Lagrangian technique combined with a mortar algorithm for modelling mechanical contact problems”. FJ Cavalieri and A Cardona. In: International Journal for Numerical Methods in Engineering. No. 4, Vol. 93, 2013, pp. 420–442. Wiley Online Library. DOI: 10.1002/nme.4391. ALM combined with a mortar algorithm (§4.3.1)
[PhDYas11] “Computational contact mechanics: geometry, detection and numerical techniques”. Vladislav A. Yastrebov. 2011. contact states, discretisation methods, detection (§4.1–4.2, §4.4)
[BookYas13] Numerical Methods in Contact Mechanics. Vladislav A. Yastrebov. Wiley-ISTE. 1st ed. 2013. numerical methods in contact mechanics (§4.2, §4.3.4)
[PhDGit12] “A dual mortar formulation for finite deformation frictional contact problems including wear and thermal coupling”. Markus Gitterle. 2012. frictional dual mortar formulation, objective slip (§4.3.4)
[BookWri06] Computational Contact Mechanics. Peter Wriggers. Springer. 2nd. 2006. computational contact mechanics (general reference)
[BookLau10] Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Tod A. Laursen. Springer. 2010. computational contact and impact mechanics (general reference)
[ArtPT92] “A mixed formulation for the finite element solution of contact problems”. Panayiotis Papadopoulos and Robert L Taylor. In: Computer Methods in Applied Mechanics and Engineering. No. 3, Vol. 94, 1992, pp. 373–389. Elsevier. DOI: 10.1016/0045-7825(92)90061-N. nodal normal averaging for the mortar geometry (§4.6.1.4)
[ArtPL04] “A mortar segment-to-segment contact method for large deformation solid mechanics”. Michael A. Puso and Tod A. Laursen. In: Computer Methods in Applied Mechanics and Engineering. No. 6–8, Vol. 193, 2004, pp. 601–629. Elsevier. DOI: 10.1016/j.cma.2003.10.010. 3D mortar method for solid mechanics (§4.2.2.4)
[ArtYL08] “A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulations”. Bin Yang and TodA. Laursen. In: Computational Mechanics. No. 2, Vol. 41, 2008, pp. 189–205. Springer-Verlag. DOI: 10.1007/s00466-006-0116-z. contact search with bounding volumes and k-DOP (§4.4.2)
[ArtRom11] “Advanced methods for robot-environment interaction towards an industrial robot aware of its volume”. Fabrizio Romanelli. In: Journal of Robotics. Vol. 2011, 2011, Hindawi. DOI: 10.1155/2011/389158. separating axis theorem for OBB (§4.4.2.1.2)
[BookEbe99] Dynamic collision detection using oriented bounding boxes. David Eberly. 1999. dynamic collision detection with oriented bounding boxes (§4.4.2.1)
[BookZZT13] The Finite Element Method: its Basis and Fundamentals. O. C. Zienkiewicz, J.Z. Zhu, and Robert L. Taylor. Butterworth-Heinemann. 7th ed. 2013. finite element method fundamentals, SPR (§4.3.3.4.1, Ch. 6)
[ArtTP] “On a patch test for contact problems in two dimensions”. Robert L. Taylor and Panagiotis Panagiotopoulos. In: . , Taylor patch test (§4.5.2, App. A.2.2.2)
[ArtHer82] “Über die berührung fester elastische Körper und über die Harte”. H Hertz. In: Verhandlungen des Vereins zur Beförderung des Gewerbefleisses. 1882, Hertz contact theory (§4.1.1, §4.5.4)
[ArtDon99] “A simple benchmark problem to test frictional contact”. CY Dong. In: Computer methods in applied mechanics and engineering. No. 1-2, Vol. 177, 1999, pp. 153–162. Elsevier. DOI: 10.1016/S0045-7825(98)00377-6. pure friction benchmark (§4.5.3)
[ArtHec+09] “Freefem++, ver. 3.7”. F Hecht, O Pironneau, A Le Hyaric, and K Ohtsuka. In: . 2009, FreeFem++ (App. C)

Complete list

Books (31)

  • [BookAkh88] The calculus of variations. Naum Ilich Akhiezer. CRC Press. 1988.
  • [BookAnd01] From Convexity to Nonconvexity. Anders Klarbring (auth.) R. P. Gilbert P. D. Panagiotopoulos P. M. Pardalos (eds.) Lars-Erik Andersson. Springer US. 1st ed. 2001.
  • [BookBAL03] Friction & flow stress in forming & cutting. Philippe Boisse, Taylan Altan, and Kees van Luttervelt. Sterling, VA: Kogan Page. 2003.
  • [BookBBT01] The friction and lubrication of solids. Frank Philip Bowden, Frank Philip Bowden, and David Tabor. Oxford university press. 2001.
  • [BookBel+14] Nonlinear Finite Elements for Continua and Structures. Ted Belytschko, Wing Kam Liu, Brian Moran, and Khalil Elkhodary. Wiley. 2nd ed. 2014.
  • [BookBHS07] Encyclopedia of Computational Mechanics (3 Volume Set). René de Borst, T.J.R. Hughes, and Erwin Stein. Wiley. 1st ed. 2007.
  • [BookBou85] Application des potentiels à l’étude de l’équilibre et du mouvement des solides élastiques. Joseph Boussinesq. Gauthier-Villars, Imprimeur-Libraire. 1885.
  • [BookCA01] Introduction to finite element methods. Felippa C.A. 2001.
  • [BookEbe99] Dynamic collision detection using oriented bounding boxes. David Eberly. 1999.
  • [BookEri04] Real-time collision detection. Christer Ericson. CRC Press. 2004.
  • [BookFSS12] OpenDSA: a creative commons active-ebook (abstract only). Eric Fouh, Maoyuan Sun, and Clifford Shaffer. 2012. Pp. 721–721.
  • [BookHBC09] Isogeometric Analysis: Toward Integration of CAD and FEA. T.J.R. Hughes, Yuri Bazilevs, and J. Austin Cottrell. Wiley. 1st ed. 2009.
  • [BookHug+14] Computer graphics: principles and practice. John F Hughes, Andries Van Dam, James D Foley, Morgan McGuire, Steven K Feiner, and David F Sklar. Pearson Education. 2014.
  • [BookIK08] Lagrange multiplier approach to variational problems and applications. Kazufumi Ito and Karl Kunisch. Siam. 2008.
  • [BookJo16] Automation of Finite Element Methods. Peter Wriggers (auth.) Joe Korelc. Springer International Publishing. 1st ed. 2016.
  • [BookKO88] Contact problems in elasticity: a study of variational inequalities and finite element methods. Noboru Kikuchi and John Tinsley Oden. siam. 1988.
  • [BookLau10] Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Tod A. Laursen. Springer. 2010.
  • [BookLei04] Dynamics and Bifurcations of Non-Smooth Mechanical Systems. Professor Dr. Henk Nijmeijer (auth.) Dr. Remco I. Leine. Springer-Verlag Berlin Heidelberg. 1st ed. 2004.
  • [BookMau13] Contact, adhesion and rupture of elastic solids. Daniel Maugis. Springer Science & Business Media. 2013.
  • [BookPhD06] R-Trees: Theory and Applications. Alexandros Nanopoulos PhD Apostolos N. Papadopoulos PhD Yannis Theodoridis PhD (auth.) Yannis Manolopoulos PhD. Springer-Verlag London. 1st ed. 2006.
  • [BookPop10] Contact Mechanics and Friction: Physical Principles and Applications. Valentin L. Popov. Springer-Verlag Berlin Heidelberg. 1st ed. 2010.
  • [BookSE02] Geometric tools for computer graphics. Philip Schneider and David H Eberly. Elsevier. 2002.
  • [BookSK13] Computational Contact Mechanics: Geometrically Exact Theory for Arbitrary Shaped Bodies. Karl Schweizerhof and Alexander Konyukhov. Springer-Verlag Berlin Heidelberg. 1st ed. 2013.
  • [BookTos05] Domain Decomposition Methods — Algorithms and Theory. Andrea Toselli Olof B. Widlund (auth.) Springer-Verlag Berlin Heidelberg. 1st ed. 2005.
  • [BookWoh01] Discretization Methods and Iterative Solvers Based on Domain Decomposition. Barbara I. Wohlmuth. Springer-Verlag Berlin Heidelberg. 1st ed. 2001.
  • [BookWP99] New Developments in Contact Problems. Peter Wriggers and Panagiotis Panagiotopoulos. Springer-Verlag Wien. 1st ed. 1999.
  • [BookWri06] Computational Contact Mechanics. Peter Wriggers. Springer. 2nd. 2006.
  • [BookWri08] Nonlinear finite element methods. Peter Wriggers. Springer. 1st ed. 2008.
  • [BookYas13] Numerical Methods in Contact Mechanics. Vladislav A. Yastrebov. Wiley-ISTE. 1st ed. 2013.
  • [BookZTF14] The Finite Element Method for Solid and Structural Mechanics. O. C. Zienkiewicz, Robert L. Taylor, and David Fox. Butterworth-Heinemann. 7th ed. 2014.
  • [BookZZT13] The Finite Element Method: its Basis and Fundamentals. O. C. Zienkiewicz, J.Z. Zhu, and Robert L. Taylor. Butterworth-Heinemann. 7th ed. 2013.

Journal articles and proceedings (102)

  • [ArtAC91] “A mixed formulation for frictional contact problems prone to Newton like solution methods”. P. Alart and A. Curnier. In: Computer Methods in Applied Mechanics and Engineering. No. 3, Vol. 92, 1991, pp. 353–375. DOI: 10.1016/0045-7825(91)90022-X.
  • [ArtAHU58] “Studies in linear and non-linear programming”. Kenneth J Arrow, Leonid Hurwicz, and Hirofumi Uzawa. In: . 1958, Cambridge Univ. Press.
  • [ArtAla88] “Multiplicateurs “augmentés” et méthode de Newton généralisée pour contact avec frottement”. P Alart. In: Report, Document LMA-DME-EPFL, Lausanne. 1988,
  • [ArtAla97] “Méthode de Newton généralisée en mécanique du contact”. Pierre Alart. In: Journal de mathématiques pures et appliquées. No. 1, Vol. 76, 1997, pp. 83–108. Elsevier.
  • [ArtAnt17] “A further analysis on the analogy between friction and plasticity in Solid Mechanics”. Nicolas Antoni. In: International Journal of Engineering Science. Vol. 121, 2017, pp. 34–51. Elsevier. DOI: 10.1016/j.ijengsci.2017.08.012.
  • [ArtAS58] “Gradient methods for constrained maxima, with weakened assumptions”. KENNETH J Arrow and ROBERT M Solow. In: Studies in linear and nonlinear programming. 1958, pp. 166–176. Stanford University Press, Stanford, CA.
  • [ArtAur+10] “Isogeometric collocation methods”. F Auricchio, L Beirao Da Veiga, TJR Hughes, A_ Reali, and G Sangalli. In: Mathematical Models and Methods in Applied Sciences. No. 11, Vol. 20, 2010, pp. 2075–2107. World Scientific. DOI: 10.1142/S0218202510004878.
  • [ArtBar08] “Adhesive elastic contacts – JKR and more”. Etienne Barthel. In: Journal of Physics D: Applied Physics. Vol. 41, 2008, p. 163001. IOP Publishing. DOI: 10.1088/0022-3727/41/16/163001.
  • [ArtBBP] “Efficient 3D data transfer operators based on numerical integration”. Philippe Bussetta, Romain Boman, and Jean-Philippe Ponthot. In: International Journal for Numerical Methods in Engineering. No. 3-4, , pp. 892–929. Wiley Online Library. DOI: 10.1002/nme.4821.
  • [ArtBen+11] “A large deformation, rotation-free, isogeometric shell”. D.J. Benson, Y. Bazilevs, M.-C. Hsu, and T.J.R. Hughes. In: Computer Methods in Applied Mechanics and Engineering. No. 13, Vol. 200, 2011, pp. 1367–1378. Elsevier. DOI: 10.1016/j.cma.2010.12.003.
  • [ArtBMP] “The adapted augmented Lagrangian method: a new method for the resolution of the mechanical frictional contact problem”. Philippe Bussetta, Daniel Marceau, and Jean-Philippe Ponthot. In: Computational Mechanics. No. 2, , pp. 259–275. DOI: 10.1007/s00466-011-0644-z.
  • [ArtBT39] “The area of contact between stationary and moving surfaces”. Frank Philip Bowden and David Tabor. In: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. No. 938, Vol. 169, 1939, pp. 391–413. The Royal Society London.
  • [ArtCai+14] “Collision detection using axis aligned bounding boxes”. Panpan Cai, Chandrasekaran Indhumathi, Yiyu Cai, Jianmin Zheng, Yi Gong, Teng Sam Lim, and Peng Wong. In: . 2014, pp. 1–14. Springer. DOI: 10.1007/978-981-4560-32-0_1.
  • [ArtCam15] “Computational modeling and simulation of rupture of membranes and thin films”. Eduardo MB Campello. In: Journal of the Brazilian Society of Mechanical Sciences and Engineering. No. 6, Vol. 37, 2015, pp. 1793–1809. Springer. DOI: 10.1007/s40430-014-0273-5.
  • [ArtCC12] “An augumented lagrangian method to solve three-dimensional nonlinear contact problems”. FJ Calavalieri and Alberto Cardona. In: Latin American applied research. No. 3, Vol. 42, 2012, pp. 281–289. SciELO Argentina.
  • [ArtCC13a] “Three-dimensional numerical solution for wear prediction using a mortar contact algorithm”. Federico José Cavalieri and Alberto Cardona. In: International Journal for Numerical Methods in Engineering. No. 8, Vol. 96, 2013, pp. 467–486. Wiley Online Library. DOI: 10.1002/nme.4556.
  • [ArtCC13b] “An augmented Lagrangian technique combined with a mortar algorithm for modelling mechanical contact problems”. FJ Cavalieri and A Cardona. In: International Journal for Numerical Methods in Engineering. No. 4, Vol. 93, 2013, pp. 420–442. Wiley Online Library. DOI: 10.1002/nme.4391.
  • [ArtCC15] “Numerical solution of frictional contact problems based on a mortar algorithm with an augmented Lagrangian technique”. F. J. Cavalieri and A. Cardona. In: Multibody System Dynamics. No. 4, Vol. 35, 2015, pp. 353–375. DOI: 10.1007/s11044-015-9449-8.
  • [ArtCFC12] “Un algoritmo de contacto mortar aplicable a problemas tridimensionales”. F.J. Cavalieri, V.D. Fachinotti, and A. Cardona. In: Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería. No. 2, Vol. 28, 2012, pp. 80–92. DOI: 10.1016/j.rimni.2012.03.001.
  • [ArtCho+05] “An improved interface element with variable nodes for non-matching finite element meshes”. Young-Sam Cho, Sukky Jun, Seyoung Im, and Hyun-Gyu Kim. In: Computer Methods in Applied Mechanics and Engineering. No. 27-29, Vol. 194, 2005, pp. 3022–3046. Elsevier. DOI: 10.1016/j.cma.2004.08.002.
  • [ArtCho+17] “An overview of recent results on Nitsche’s method for contact problems”. Franz Chouly, Mathieu Fabre, Patrick Hild, Rabii Mlika, Jerome Pousin, and Yves Renard. In: . 2017, pp. 93–141. Springer.
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  • [ArtDB06] “Information transfer between incompatible finite element meshes: application to coupled thermo-viscoelasticity”. David Dureisseix and Henri Bavestrello. In: Computer Methods in Applied Mechanics and Engineering. No. 44-47, Vol. 195, 2006, pp. 6523–6541. Elsevier. DOI: 10.1016/j.cma.2006.02.003.
  • [ArtDB15] “A literature review of bounding volumes hierarchy focused on collision detection”. Simena Dinas and José M Bañón. In: Ingeniería y competitividad. No. 1, Vol. 17, 2015, pp. 49–62. Universidad del Vall.
  • [ArtDem+12] “Computational comparison of the bending behavior of aortic stent-grafts”. Nicolas Demanget, Stéphane Avril, Pierre Badel, Laurent Orgéas, Christian Geindreau, Jean-Noël Albertini, and Jean-Pierre Favre. In: Journal of the mechanical behavior of biomedical materials. No. 1, Vol. 5, 2012, pp. 272–282. Elsevier. DOI: 10.1016/j.jmbbm.2011.09.006.
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  • [ArtDon99] “A simple benchmark problem to test frictional contact”. CY Dong. In: Computer methods in applied mechanics and engineering. No. 1-2, Vol. 177, 1999, pp. 153–162. Elsevier. DOI: 10.1016/S0045-7825(98)00377-6.
  • [ArtDPS] “A frictional mortar contact approach for the analysis of large inelastic deformation problems”. T Doca, FM Andrade Pires, and JMA Cesar de Sa. In: International Journal of Solids and Structures. No. 9, , pp. 1697–1715. Elsevier. DOI: 10.1016/j.ijsolstr.2014.01.013.
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  • [ArtFW06] “Mortar based frictional contact formulation for higher order interpolations using the moving friction cone”. Kathrin A Fischer and Peter Wriggers. In: Computer methods in applied mechanics and engineering. No. 37-40, Vol. 195, 2006, pp. 5020–5036. Elsevier. DOI: 10.1016/j.cma.2005.09.025.
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  • [ArtHer82] “Über die berührung fester elastische Körper und über die Harte”. H Hertz. In: Verhandlungen des Vereins zur Beförderung des Gewerbefleisses. 1882,
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  • [ArtLWZ12a] “A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method”. L. de Lorenzis, Peter Wriggers, and G. Zavarise. In: Computational Mechanics. No. 1, Vol. 49, 2012, pp. 1–20. Springer. DOI: 10.1007/s00466-011-0623-4.
  • [ArtLWZ12b] “A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method”. L. De Lorenzis, Peter Wriggers, and G. Zavarise. In: Computational Mechanics. No. 1, Vol. 49, 2012, pp. 1–20. Springer-Verlag. DOI: 10.1007/s00466-011-0623-4.
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PhD theses (9)

  • [PhDBru08] “Contact analysis and overlapping domain decomposition methods for dynamic and nonlinear problems”. Stephan BrunSSen. 2008.
  • [PhDBus] “Modélisation et résolution du problème de contact mécanique et son application dans un contexte multiphysique”. Philippe Bussetta.
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  • [PhDHam13] “Frictional mortar contact for finite deformation problems with synthetic contact kinematics”. Michael E. Hammer. 2013.
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  • [PhDPop12] “Mortar Methods for Computational Contact Mechanics and General Interface Problems”. Alexander Popp. 2012.
  • [PhDYas11] “Computational contact mechanics: geometry, detection and numerical techniques”. Vladislav A. Yastrebov. 2011.

Online resources (4)

  • V. Mataix Ferrándiz, Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method, PhD thesis, Universitat Politècnica de Catalunya, 2020. Directors: E. Oñate, R. Rossi. UPCommons.
  • P. Dadvand, R. Rossi, E. Oñate, An object-oriented environment for developing finite element codes for multi-disciplinary applications, Archives of Computational Methods in Engineering 17 (2010) 253–297. DOI: 10.1007/s11831-010-9045-2 — the Kratos framework.
  • P. Dadvand, R. Rossi, M. Gil, X. Martorell, J. Cotela, E. Juanpere, S. R. Idelsohn, E. Oñate, Migration of a generic multi-physics framework to HPC environments, Computers & Fluids 80 (2013) 301–309. DOI: 10.1016/j.compfluid.2012.02.004.

See also the Glossary for the acronyms used throughout the documentation.