Subproject C2

Bond Behaviour of Shell Strengthenings

Director

Prof. Dr.-Ing. Bernd W. Zastrau
Institute of Mechanics and Shell Structures

Scientific Staff

Dr.-Ing. Rainer Schlebusch
Dipl.-Ing. Jan Matheas

Aims and cooperation

The here on the basis of surface-related shell theories developed and still to develop finite element-models refer to shell structure of textile-reinforced concrete - mainly with regard to the integration into the SFB - although the methodical accesses are material-neutral. The research concentrates on the theoretical and numerical aspects of the deduction of surface-related shell theories and shell elements respectively volume-shell elements as well as their integration into an efficient finite element-program package. The main focus of the work is given on the application of contact-mechanics to describe the layer bond particularly connected with surface-related multi-layer multi-director shell elements. These ones possess as opposed to the proceeding in other research work no displacement-fields steady over the layers, but admit - under kinematical points of view - a free, respectively through laws of contact-kinematics and the layer bond restricted displacement of the layers among each other, cp. figure 4. In the limelight is the investigation of contact-stress state and delamination, cp. figure 1 (experiments in the TP D1), first between basic material and strengthening, and second in any surfaces of the bond-surfaces within the strengthening, cp. figure 2.

[Removed image: http://rcswww.urz.tu-dresden.de/%7Emechanik/forschung/schalentheorie/img/schdelam_en.png Alternative text: Image caption: ]

Figure 1: Delamination at a strenghtening from textile reinforced concrete - experiments in TP D1

[Removed image: http://rcswww.urz.tu-dresden.de/%7Emechanik/forschung/schalentheorie/img/schschichtg_en.png Alternative text: Image caption: ]

Figure 2: Layer properties of the reinforced structure and characterisation of the damage types, here at textile reinforced concrete

Utilisation-oriented aim of this research project is the determination of the stress state in the strengthening layer of curved structures (cp. figure 3) and to give a contribution to the design of the textile reinforcement through optimisation of the main direction and application of the material, i. e. the directions and the quantity of the fibers in the strengthening layer.

[Removed image: http://rcswww.urz.tu-dresden.de/%7Emechanik/forschung/schalentheorie/img/kruemmel.png Alternative text: Image caption: ]

Figure 3: Cupola of the water tower in Krümmel to restaurate

[Removed image: http://rcswww.urz.tu-dresden.de/%7Emechanik/forschung/schalentheorie/img/schmskine_en.png Alternative text: Image caption: ]

Figure 4: Material independant damage model

Model-adaptivity
To consider the delamination, in the further development a model-adaptivity is striven for. This means an automatic adjustment of the kinematics based upon sliding surfaces "parallel" to shell reference surface, determined by the application of an inelastic material-law. Starting out from an one-layer kinematics, in those elements will be switched to the multilayer shell kinematics, in which the three-dimensional stress states reach the damage-limit of the material-law at some points of the shell continuum. The bond-surfaces orientate on the shear-planes. So, multilayer elements can result, whereby one single layer in the element can be floated completely or partially from the adjoining one.

Inelastic material-law
An inelastic material-law, of which the development is planned in the TP A3, has to be implemented into the existing shell model. The simultaneous application of inelastic material-laws in the shell-continuum and the multilayer kinematics with moveable layers makes it possible to describe separately the two effects delamination and inclined-crack-formation determined in bond-experiments of the TP C1.

Development of the contact-bond-law
Connected with the description of the bond another focal point is the more exact investigation of contact-surfaces with regard to contact-mechanics, i.e. the delaminated as well as not delaminated area in the multilayer bond-model, therefore a curved restricted surface independent from discretisation. The evaluation of the damage-criterion only at the integration-points is not sufficient if few big elements are applied.

Optimisation the strengthening layer
Furthermore it is intended to find strategies for the optimisation of the strengthening layer regarding the material-application at any curved shell structure. The determination of suitable textile structures, based on the determination of optimal values for efficient macroscopic material parameters, is planned in the TP A3 and supported by the selection of suitable calculation-procedures in the TP C2. For that, common optimisation-procedures should be applied. The values of the parameters of the material-law for the load-bearing structure are found in iterative processes by using simple objective functions, as for example a certain exploitation-degree of the allowed stress state (damage-limit) in the points of the shell continuum. Those ones can be used to modify the number and the order of the textile-lay-ups in the TP A3 then.

Results

A description of the behaviour after the crack was enabled by introduction of the multilayer shell theories with integrated contact-conditions. Figure 5 shows the test arrangement chosen in the TP C1 of the pull-off of a textile-reinforced concrete-slat from a concrete-prism of the strength-class B25. The part of the test-bodies marked in this figure as discretised area has been discretised for the calculation of the displacement and stress state (shown in figure 6) in altogether 144 finite shell elements, of them in each case 72 one- and two-layered, exploiting the symmetry of the arrangement of the experiment concerning the displacement. Figure 7 shows a crack-pattern of the bond-area as a result of the bond-experiment of the TP C1, with which the textile-reinforced fine-grained concrete-layer was pulled off from the basic body (to the left), cp. the bond-area of the corresponding test arrangement (marked in figure 5).

[Removed image: http://rcswww.urz.tu-dresden.de/%7Emechanik/forschung/schalentheorie/img/schc1versuch_en.png Alternative text: Image caption: ]

Figure 5: Test arragement of the slat pull-off experiment of the TP C1

[Removed image: http://rcswww.urz.tu-dresden.de/%7Emechanik/forschung/schalentheorie/img/schnumsim_en.png Alternative text: Image caption: ]

Figure 6: Numeric simulation of the slat pull-off experiment at the discretised area of figure 5 - Distribution at F=31,21 kN of the displacements (top), shear stress (bottom) in a cut along the load direction in the discretised area

Delamination as a damage type was described for multilayer shells by using contact mechanics. Based on a tension-criterion (also called bond-condition) the kinematics used for the shell element are switched from such ones with steady displacement-fields over the shell thickness direction to kinematics with discontinuous displacement-fields (if necessary) during the iterative solution-process of the equation-system of the FEM. The kinematic relations ensure the connection of the layers as long as critical tensions (cp. figure 7 in the middle) that result in delamination, were not yet reached at a determined point in the interface between two layers. For the behaviour after the crack, i. e. here after the delamination, there are used the common conditions of the contact-mechanics, the restriction of penetration and a friction law fitted for the requirements of the description of adhesion (cp. figure 7).

[Removed image: http://rcswww.urz.tu-dresden.de/%7Emechanik/forschung/schalentheorie/img/schrissbild_en.png Alternative text: Image caption: ]

Figure 7: Crack-pattern of the experiments und stress state limits of the model

Publications

2008

• Kula, K.; Kuczma, M.; Schlebusch, R.; Zastrau, B.: Application and Mechanics of Fibre-Reinforced Composites. In: Walter Schmitz (Hrsg.): Ein anderes Europa. Innovation-Anstöße-Tradition in Mittel- und Osteuropa. Dokumentation zum 3. Sächsischen Mittel- und Osteuropatag. Aus der Reihe: Mitteleuropa Aktuell 2, Dresdner Wissenschaftsverlage Thelem, 2008, S. 578-589
• Schlebusch, R.; Zastrau, B.: On a Surface-Related Shell Formulation for the Numerical Simulation of Textile Reinforced Concrete Layers. In: Kotulski, Z.; Kowalczyk, P.; Sosnowski, W. (eds.): Selected Topics of Contemporary Solid Mechanics. Proceedings of the 36th Solid Mechanics Conference (SolMech2008), 2008, Gdansk, Poland. 2 pp.
• Schlebusch, R.; Zastrau, B.: On the Simulation of Textile Reinforced Concrete Layers by a Surface-Related Shell Formulation. In: George Jaiani, Paolo Podio-Guidugli (eds.): IUTAM Symposium on Relation of Shell, Beam, and 3D Models, Proceedings of the IUTAM Symposium on Relation of Shell, Beam, and 3D Models. Tbilisi, Georgia, Tbilisi State University, IUTAM Bookseries, Vol. 9, New-York : Springer, 2008, pp. 189-198
• Zastrau, B.; Schlebusch, R.; Kula, K.;Matheas, J.: Numerical Simulation of Composite´s Interface Failure – Delamination. In: 8th Congress on Computational Mechanics (WCCM8), 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), Venice, Italy, 2008. 2 pp.
• Zastrau, B.; Schlebusch, R.: Utilization of the Assumed Natural Strain Method in a Surface-Related Solid-Shell Element. In: Abel, J. F.; Cooke, J. R. (eds.): Proceedings of the 6th International Conference on Computation of Shell & Spatial Structures: IASS-IACM 2008 – "Spanning Nano to Mega", Cornell University, Ithaca, New York, 2008. 4 pp.

2007

• Schlebusch, R.; Zastrau, B.: Adaptation of the Assumed Natural Strain Method for Application in a Surface-Related Shell Formulation. In: 6th German-Greek-Polish Symposium "Recent Advances in Mechanics", Alexandroupolis, Greece, 2007. 2 pp.
• Schlebusch, R.; Zastrau, B.: Adaptation of the Assumed Natural Strain Method for Application in a Surface-Related Shell Formulation. In: The Third International Conference on Structural Engineering, Mechanics and Computation, Cape Town, South Africa, 2007. 6 pp. and CD-ROM Proceedings
• Zastrau, B.; Schlebusch, R.: Adaptation of the Assumed Natural Strain Method for Application in a Surface-Related Shell Formulation. In: 9th U.S National Congress on Computational Mechanics, San Francisco, USA, 2007. Abstract 1 p.
• Kuczma, M.; Kula, K., Schlebusch, R.; Zastrau, B.: Numerical Simulation of thin Composite Structures with Delamination. In: Proceedings of the 17th International Conference on Computer Methods in Mechanics CMM-2007, Lodz-Spala, Poland, 2007. 7 pp.

2006

• Matheas, J.: Delamination/Bruch in der Grenzfläche von Beton und Textilbeton mit Kontakt und Reibung. In: Wagner, W. (Hrsg.): Technische Sicherheit, Zuverlässigkeit und Lebensdauer, 38. Tagung des DVM-Arbeitskreises Bruchvorgänge. Aachen, 2006, S. 117-126 – ISSN 1616-4687
• Schlebusch, R.; Matheas, J.; Zastrau, B.: Aspekte eines oberflächenorientierten finiten Volumen-Schalen-Element. In: Forschungskolloquium Baustatik-Baupraxis, Obergurgl, Österreich, 2006. 1 Abstract 1 p.
• Matheas, J.; Schlebusch, R.; Zastrau B.: Delamination in the Interface of Textile Reinforced Concrete Layers with Contact and Friction. In: Hegger, J.; Brameshuber, W.; Will, N. (Hrsg.): Textile Reinforced Concrete. Proceedings of the First International Conference on Textile Reinforced Concrete (ICTRC), Internationales Fachkolloquium der Sonderforschungsbereiche 528 und 532, 5.-7. Aachen, Deutschland. Bagneux, Frankreich : RILEM Publications S.A.R.L., 2006, pp. 233-242
• Zastrau, B.; Schlebusch, R.: Adaptation of the Assumed Natural Strain Method for Application in a Surface-Related Shell Formulation. In: Willner, K.; Hanss, M. (Hrsg.): Angewandte und Experimentelle Mechanik – Ein Querschnitt. Berichte aus dem Institut für Angewandte und Experimentelle Mechanik der Universität Stuttgart, Heft 3, Tönning : Der Andere Verlag, 2006, S. 317-342.
• Schlebusch, R.; Zastrau, B.: Theory and Numerics of a Surface-Related Shell Formulation. In: C.A. Mota Soares et al. (eds.): 3th European Conference on Computational Mechanics–Solids, Structures and Coupled Problems in Engineering, Lisboa. Dordrecht, The Netherlands : Springer, 2006, pp. 1-16, CD-ROM Proceedings.

2005

• Zastrau, B.; Lepenies, I.; Matheas, J.; Zarzour, H.: Verstärkung der Stahlbetonkuppel des Krümmeler Wasserturms mit Textilbeton. In: Möller, B. (Hrsg.): Baustatik-Baupraxis 9. Dresden, 2005, S. 117-128 – (ISBN 3-00-015456-6)
• Schlebusch, R.; Zastrau, B.: Variational Formulation and Numerical Treatment of a Surface-Related Solid-Shell Element. In: Proceedings of the Third M. I. T. Conference on Computational Fluid and Solid Mechanics. Cambridge, MA, USA, 14.-17. Juni 2005, Elsevier Science Ltd., Oxford, Großbritannien, 2005, S. 327
• Schlebusch, R.; Zastrau, B.: On Numerical Treatment of a Surface-Related Solid-Shell Element. In: IASS-IACM 2005, Fifth International Colloquium on Computation of Shell & Spatial Structures. Salzburg, Österreich, 1.-4. Juni 2005, CD-Proceedings, 2005, 4 S.
• Schlebusch, R.; Zastrau, B.: On Numerical Treatment of a Surface-Related Solid-Shell Element. In: Pietraszkiewicz, W.; Szymczak, C.: Proceedings of the 8th Conference on Shell Structures – Theory and Applications (SSTA 2005). Gdansk University of Technology, Gdansk-Jurata, Polen, Taylor & Francis/Balkema, London, 2005, S. 503-506 – ISBN 0415-38390-0
• Schlebusch, R.: Theorie und Numerik einer oberflächenorientierten Schalenformulierung. Berichte des Instituts für Mechanik und Flächentragwerke, Heft 3, 2005, Dresden : Technische Universität Dresden, Dissertation – urn:nbn:de:swb:14-1137572448296-67009

2004

• Chudoba, R.; Graf, W.; Meskouris, K.; Zastrau, B.: Numerische Modellierung von textilverstärktem Beton. Beton- und Stahlbetonbau 99 (2004) 6, S. 460-465 – doi:10.1002/best.200490117
• Schlebusch, R.; Matheas, J.; Zastrau, B.: On the Numerical Simulation of Thin Textile Reinforced Concrete Layers for the Strengthening of Shell Structures Using a Surface-Related Shell Theory. In: Kienzler, R.; Altenbach, H.; Ott, I. (Hrsg.): Lecture Notes in Applied and Computational Mechanics, Theories of Plates and Shells. 16 (2004), Springer-Verlag, Berlin, S. 211-218 (ISBN 3-540-20997-2)
• Chudoba, R.; Graf, W.; Meskouris, K.; Zastrau, B.: Numerische Modellierung von textilbewehrtem Beton. In: Beton- und Stahlbetonbau 99 (2004) 6, S. 460-465

2003

• Zastrau, B.; Matheas, J.; Schlebusch, R.: Oberflächenorientierte Multidirektor-Mehrschichten-Schalenmodelle. In: Curbach, M. (Edt.): Textile Reinforced Structures. Proceedings of the 2nd Colloqium on Textile Reinforforced Structures (CTRS2), Dresden, Germany, 29.9.2003–1.10.2003. Dresden : Sonderforschungsbereich 528, Technische Universität Dresden, 2003, S. 411–422 (ISBN 3-86005-386-8)
• Zastrau, B.; Schlebusch, R.; Matheas, J.: Special aspects of surface-related shell theories with application to contact problems. In: Bathe, K., J.: Computational Fluid and Solid Mechanics 2003, V. 1, Elsevier Science Ltd., Oxford, UK, 2003, S. 787–790 (ISBN 0 08 044046 0)
• Schlebusch, R.: Nonlinear Surface-Related Shell Theories - Theoretical and Numerical Aspects. In: Proceedings in Applied Mathematics and Mechanics 2 (2003) 1, 260-261 – doi:10.1002/pamm.200310424
• Schlebusch, R.; Matheas, J.; Zastrau, B.: On surface-related shell theories for the numerical simulation of contact problems. In: Journal of Theoretical and Applied Mechanics 3 (2003) 41, S. 623-642 (ISSN 1429-2955)
• Matheas, J.; Schlebusch, R.; Zastrau, B.: On a Surface-Related Multi-Layer Shell Theory and its Application to Compound Structures. In: Proceedings in Applied Mathematics and Mechanics 3 (2003) 1, 304-305 – doi:10.1002/pamm.200310424
• Matheas, J.; Schlebusch, R.; Zastrau, B.: Mechanisches Modell und numerische Simulation von Flächentragwerken mit Verstärkung aus Textilbeton. In: Gebbeken, N. (Hrsg.): Berichte aus dem Konstruktiven Ingenieurbau, Aktuelle Beiträge aus Baustatik und Comp. Mechanics. 03/3 (2003), Universität der Bundeswehr München, Neubiberg, S. 313-325 (ISSN 1431-5122)
• Zastrau, B.; Lepenies, I.; Matheas, J.; Richter, M.; Schlebusch, R.: Textilbewehrter Beton – von der Beschreibung des Materialverhaltens zur Entwicklung einer adäquaten Schalentheorie. In: Zastrau, B.; Gebbeken, N.; Kaliske, M.; Nasdala, L. (Hrsg.): Berichte des Instituts für Mechanik und Flächentragwerke, Jubiläumsschrift H. Rothert. 1 (2003), Technische Universität Dresden, Dresden, S. 159-177 (ISBN 3-86005-395-7)

2002

• Zastrau, B.; Lepenies, I.; Matheas, J.; Richter, M.; Schlebusch, R.: Zur Modellierung und Berechnung von Flächentragwerken mit flächiger Verstärkung aus textilbewehrtem Feinbeton. In: Dinkler, D. (Hrsg.): Baustatik-Baupraxis 8. Braunschweig, 2002, S. 175–188
• Schlebusch, R.; Matheas J.; Zastrau, B.: On the avoidance of Poisson thickness locking in surface-related shell theory by an extension of the EAS method. In: Machine Dynamics Problems 26, Nr. 4, Warsaw University of Technology, Warschau, 2002, S. 101-114 (ISSN 0239-7730)
• Schlebusch, R.; Matheas, J.; Zastrau, B.: A Three-Dimensional Surface-Related Shell Theory for the Treatment of Contact Problems. In: Mang, H. A.; Rammerstorfer, F. G.; Eberhardsteiner, J.: Fifth World Congress on Computational Mechanics (WCCM V), July 7-12, 2002, Vienna University of Technology. Wien, Österreich, 2002, S. 560, CD 10 S., http://wccm.tuwien.ac.at (ISBN 3-9501554-0-6)

2001

• Knothe, K.; Wille, R.; Zastrau, B.: Advanced Contact Mechanics – Road and Rail. In: International Journal of Vehicle Mechanics and Mobility 35 (2001), 4/5, S. 361–407
• Matheas, J.; Schlebusch, R.; Zastrau, B. W.: Zur Herleitung einer oberflächenorientierten Schalentheorie und deren Umsetzung im Rahmen der Finite-Element-Methode. In: 1. Fachkolloquium Textilbeton. RWTH Aachen, 2001, S. 193-204 (PDF-Datei, 787 kB)
• Nackenhorst, U.; Zastrau, B.: Numerische Parameterstudien zur Beanspruchung von Rad und Schiene beim Rollkontakt. In: EI - Eisenbahningenieur 52 (2001), H. 2, S. 48-52
• Neuberg, C.; Schlebusch, R.; Matheas, J.; Zastrau, B.: Zur Enhanced-Assumed-Strain-Methode bei oberflächenorientierten Schalentheorien zur Vermeidung von Poisson-Dickenlocking. In: Mitteilungen des Institutes für Baumechanik und Bauinformatik und des Fakultätsrechenzentrums, Nov./2001. Technische Universität Dresden, Dresden, 2001, S. 57–70
• Zastrau, B.; Schlebusch, R.; Matheas, J.: Grundlagen der Berechnung flächig verstärkter Tragwerke mittels einer oberflächenorientierten Schalentheorie. In: Festschrift zum 60. Geburtstag von Prof. Dr.-Ing. habil. Bernd Möller. Technische Universität Dresden, Dresden, 2001, S. 345–358

2000

• Zastrau, B.; Schlebusch, R.; Matheas, J.: Surface-related Shell Theories for the Treatment of Composites and Contact Problems. In: Fourth International Colloquium on Computation of Shell and Spatial Structures, 5.–7. Juni 2000. IASS-IACM 2000, Chania-Kreta, Griechenland, 2000
• Schlebusch, R.; Matheas, J.: Oberflächenorientierte Schalentheorien zur Untersuchung von Kontaktproblemen. In: Wagner, W. (Hrsg.): Forschungskolloquium Baustatik-Baupraxis, 25.-27. September 2000. Bad Herrenalb, Deutschland, 2000, S. 60-61

1999

• Curbach, M.; Zastrau, B.: Textilbewehrter Beton - Aspekte aus Theorie und Praxis. In: Meskouris, K. (Hrsg.): Baustatik Baupraxis 7, Rotterdam : Balkema, 1999, S. 267-276.