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Tytuł artykułu

Isogeometric treatment of large deformation contact and debonding problems with T-splines: a review

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
Within a setting where the isogeometric analysis (IGA) has been successful at bringing two different research fields together, i.e. Computer Aided Design (CAD) and numerical analysis, T-spline IGA is applied in this work to frictionless contact and mode-I debonding problems between deformable bodies in the context of large deformations. Based on the concept of IGA, the smooth basis functions are adopted to describe surface geometries and approximate the numerical solutions, leading to higher accuracy in the contact integral evaluation. The isogeometric discretizations are here incorporated into an existing finite element framework by using Bézier extraction, i.e. a linear operator which maps the Bernstein polynomial basis on Bézier elements to the global isogeometric basis. A recently released commercial T-spline plugin for Rhino is herein used to build the analysis models adopted in this study. In such context, the continuum is discretized with cubic T-splines, as well as with Non Uniform Rational B-Splines (NURBS) and Lagrange polynomial elements for comparison purposes, and a Gauss-point-to-surface (GPTS) formulation is combined with the penalty method to treat the contact constraints. The purely geometric enforcement of the non-penetration condition in compression is generalized to encompass both contact and mode-I debonding of interfaces which is approached by means of cohesive zone (CZ) modeling, as commonly done by the scientific community to analyse the progressive damage of materials and interfaces. Based on these models, non-linear relationships between tractions and relative displacements are assumed. These relationships dictate both the work of separation per unit fracture surface and the peak stress that has to be reached for the crack formation. In the generalized GPTS formulation an automatic switching procedure is used to choose between cohesive and contact models, depending on the contact status. Some numerical results are first presented and compared in 2D for varying resolutions of the contact and/or cohesive zone, including frictionless sliding and cohesive debonding, all featuring the competitive accuracy and performance of T-spline IGA. The superior accuracy of T-spline interpolations with respect to NURBS and Lagrange interpolations for a given number of degrees of freedom (Dofs) is always verified. The isogeometric formulation is also extended to 3D bodies, where some examples in large deformations based on T-spline discretizations show an high smoothness of the reaction history curves.
Słowa kluczowe
Wydawca
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2014-12-15
zaakceptowano
2015-01-05
online
2015-02-09
Twórcy
  • Department of Innovation
    Engineering, University of Salento, Lecce, Italy
Bibliografia
  • [1] Heegaard J.H., Curnier A., An augmented Lagrange method fordiscrete large slip contact problems, Int. J. Numer. Meth Eng.,1993, 36, 569–593.[Crossref]
  • [2] Zavarise G., De Lorenzis L., The node-to-segment algorithm for2D frictionless contact: classical formulation and special cases,Comput. Method. Appl. M., 2009, 198(41-44), 3428–3451.[Crossref]
  • [3] Pietrzak G., Curnier A., Large deformation frictional contact mechanics:continuum formulation and augmented Lagrangeantreatment, Comput. Method. Appl. M., 1999, 177, 351–381.
  • [4] Taylor R.L., Wriggers P., Smooth surface discretization for largedeformation frictionless contact, Technical report, University ofCalifornia, Berkeley, 1999, Report No. UCB/SEMM-99–04.
  • [5] Padmanabhan V., Laursen T.A., A framework for developmentof surface smoothing procedures in large deformation frictionalcontact analysis, Finite Elem. Anal. Des., 2001, 37, 173–198.
  • [6] Wriggers P., Krstulovic-Opara L., Korelc J., SmoothC1–interpolations for twodimensional frictional contactproblems, Int. J. Numer. Methods Eng., 2001, 51, 1469–1495.
  • [7] Krstulovic-Opara L., Wriggers P., Korelc J., A C1–continuous formulationfor 3D finite deformation frictional contact, Comput.Mech., 2002, 29, 27–42.
  • [8] Lengiewicz J., Korelc J., Stupkiewicz S., Automation of finite elementformulations for large deformation contact problems, Int.J. Numer. Methods Eng., 2010, 85, 1252–1279.
  • [9] Stadler M., Holzapfel G.A., Korelc J., Cn–continuous modellingof smooth contact surfaces using NURBS and application to 2Dproblems, Int. J. Numer. Methods Eng., 2003, 57, 2177–2203.[Crossref]
  • [10] Stadler M.,Holzapfel G.A., Subdivision schemes for smooth contactsurfaces of arbitrary mesh topology in 3D, Int. J. Numer.Methods Eng., 2004, 60, 1161–1195.[Crossref]
  • [11] Landon R.L., Hast M.W., Piazza S.J., Robust contact modelingusing trimmed nurbs surfaces for dynamic simulations of articularcontact, Comput. Meth. Appl. Mech. Eng., 2009, 198,2339–2346.[Crossref]
  • [12] Hughes T.J.R., Cottrell J. A., Bazilevs Y., Isogeometric analysis:CAD, finite elements, NURBS, exact geometry, and mesh refinement,Comput. Meth. Appl. Mech. Eng., 2005, 194, 4135–4195.[Crossref]
  • [13] Temizer İ., Wriggers P., Hughes T.J.R., Contact treatment in isogeometricanalysis with NURBS, Comput. Meth. Appl. Mech.Eng., 2011, 200(9–12), 1100–1112.
  • [14] Temizer İ., Wriggers P., Hughes T.J.R., Three-dimensionalmortar-based frictional contact treatment in isogeometric analysiswith NURBS, Comput. Meth. Appl. Mech. Eng., 2012,209–212, 115–128.
  • [15] Lu J., Isogeometric contact analysis: geometric basis and formulationfor frictionless contact, Comput. Meth. Appl. Mech. Eng.,2011, 200, 726–74.
  • [16] De Lorenzis L., Temizer İ.,Wriggers P., Zavarise G., A large deformationfrictional contact formulation using NURBS-based isogeometricanalysis, Int. J. Numer. Methods Eng., 2011, 87(13),1278–1300.
  • [17] De Lorenzis L.,Wriggers P., Zavarise G., A mortar formulation for3D large deformation contact using NURBS-based isogeometricanalysis and the augmented Lagrangian method, Comput.Mech., 2012, 49(1), 1–20.[Crossref]
  • [18] Matzen M.E., Cichosz T., Bischoff M., A point to segment contactformulation for isogeometric, NURBS based finite elements,Comput. Meth. Appl. Mech. Eng., 2013, 255, 27–39.
  • [19] Dimitri R., De Lorenzis L., Scott M.A., Wriggers P., Taylor R.L.,Zavarise G., Isogeometric large deformation frictionless contactusing T-splines, Comput. Meth. Appl. Mech. Eng., 2014, 269,394–414.
  • [20] De Lorenzis L., Evans J.A., Hughes T.J.R., Reali A., Isogeometriccollocation: Neumann boundary conditions and contact, Comput.Meth. Appl. Mech. Eng., 2015, 284, 21–54.
  • [21] De Lorenzis L., Wriggers P., Hughes T.J.R., Isogeometric contact:a review, GAMM-Mitt. 37, No.1, 2014, 85–123, /DOI10.1002/gamm.201410005.[Crossref]
  • [22] Alart P., Curnier A., A mixed formulation for frictional contactproblems prone to Newton like solution methods, Comput.Meth. Appl. Mech. Eng., 1991, 92, 353–375.[Crossref]
  • [23] Cottrell J. A., Hughes T.J.R., Bazilevs Y., Isogeometric Analysis:Toward Integration of CAD and FEA, Wiley, Chichester, 2009.
  • [24] Bazilevs Y., Calo V.M., Cottrell J.A., Evans J.A., Hughes T.J.R., LiptonS., Scott M.A., Sederberg T.W., Isogeometric analysis usingT-splines, Comput. Meth. Appl. Mech. Eng., 2010, 199 (5-8),229–263.[Crossref]
  • [25] Fischer K.A., Wriggers P., Frictionless 2D contact formulationsfor finite deformations based on the mortar method, Comput.Mech., 2005, 36, 226–244.[Crossref]
  • [26] Kanninen M.F., Popelar C.H., Advanced Fracture Mechanics, OxfordUniversity Press, New York, 1985.
  • [27] Bazˇant Z.P., Planas J., Fracture and Size Effects in Concrete andOther Quasi-Brittle Materials, CRC Press, Boca Raton, 1998.
  • [28] Rice J.R., A path independent integral and the approximateanalysis of strain concentration by notches and cracks, J. Appl.Mech., 1968, 35, 379–386.[Crossref]
  • [29] Rybicki E.F., Kanninen M.F., A finite element calculation of stressintensity factors by a modified crack closure integral, Eng. Fract.Mech., 1977, 9, 931–938.[Crossref]
  • [30] Raju I.S., Calculation of strain-energy release rates with higherorder and singular finite elements, Eng. Fract. Mech., 1987, 28,251–274.[Crossref]
  • [31] Hellen T.K., On the method of virtual crack extensions, Int. J. Numer.Methods Eng., 1975, 9, 187–207.[Crossref]
  • [32] Griflth A., The phenomena of rupture and flow in solids, Phil.Trans. R. Soc. A., 1921, 221, 163–198.[Crossref]
  • [33] Thouless M.D., Fracture of a model interface under mixed-modeloading, Acta Metall. Mater., 1990, 38, 1135–1140.[Crossref]
  • [34] Thouless M.D., Hutchinson J.W., Liniger E.G., Plane-strain, bucklingdriven delamination of thin films: model experiments andmode-II fracture, Acta Metall. Mater., 1992, 40, 2639–2649.[Crossref]
  • [35] Natarajan S., Ferreira A.J.M., Nguyen-Xuan H., Analysis of crossplylaminated plates using isogeometric analysis and unifiedformulation, Curved and Layer. Struct., 2014, 1, 1–10.
  • [36] Benzley S.E., Representation of singularitieswith isoparametricfinite elements, Int. J. Numer. Methods Eng., 1974, 8, 537–545.[Crossref]
  • [37] Gifford L.N., Hilton P.D., Stress intensity factors by enriched finiteelements, Eng. Fract. Mech., 1978, 10, 485–496.[Crossref]
  • [38] Sukumar N., Moran B., Black T., Belytschko T., An elementfreegalerkin method for three-dimensional fracture mechanics,Comput. Mech., 1997, 20, 170–175.[Crossref]
  • [39] Jirasek M., Zimmerman T., Embedded crack model: I. basic formulation,Int. J. Numer. Methods Eng., 2001, 50, 1269–1290.[Crossref]
  • [40] Wells G.N., Sluys L.J., A new method for modelling cohesivecracks using finite elements, Int. J. Numer. Methods Eng., 2001,50, 2667–2682.[Crossref]
  • [41] Moës N., Belytschko T., Extended finite element method for cohesivecrack growth, Eng. Fract. Mech., 2002, 69, 813–833.[Crossref]
  • [42] Moës N., Dolbow J., Belytschko T., A finite element method forcrack growth without remeshing, Int. J. Numer. Methods Eng.,1999, 46, 131–150.[Crossref]
  • [43] Sukumar N., Huang Z.Y., Prevost J.H., Suo Z., Partition of unityenrichment for bimaterial interface cracks, Int. J. Numer. MethodsEng., 2004, 59, 1075–1102.[Crossref]
  • [44] Allix O., Ladeveze P., Interlaminar interface modelling for theprediction of delamination, Compos. Struct., 1992, 22, 235-242.[Crossref]
  • [45] Schellekens J.C.J., de Borst R., A non-linear finite element approachfor the analysis of mode-I free edge delamination in composites,Int. J. Solids Struct., 1993, 30, 1239-1253.[Crossref]
  • [46] Barenblatt G.I., The formation of equilibrium cracks during brittlefracture. General ideas and hypotheses, Axially-symmetriccracks, J. Appl. Math. Mech., 1959, 23, 622–636.[Crossref]
  • [47] Dugdale D.S., Yielding of steel sheets containing slits, J. Mech.Phys. Solids, 1960, 8, 100–104.[Crossref]
  • [48] Needleman A., A continuum model for void nucleation by inclusiondebonding, J. Appl. Mech., 1987, 54, 525–531.[Crossref]
  • [49] Needleman A., An analysis of tensile decohesion along an interface,J. Mech. Phys. Solids, 1990, 38, 289– 324.[Crossref]
  • [50] Tvergaard V., Hutchinson J.W., The relation between crackgrowth resistance and fracture process parameters in elasticplasticsolids, J. Mech. Phys. Solids, 1992, 40(6), 1377–1397.[Crossref]
  • [51] Tvergaard V., Hutchinson J.W., The influence of plasticity onmixed mode interface toughness, J. Mech. Phys. Solids, 1993,41(6), 1119–1135.[Crossref]
  • [52] Wei Y., Hutchinson J.W., Interface strength, work of adhesionand plasticity in the peel test, Int. J. Fract., 1998, 93, 315–333.[Crossref]
  • [53] Corigliano A., Formulation, identification and use of interfacemodels in the numerical analysis of composite delamination,Int. J. Solids Struct., 1993, 30(20), 2779–2811.[Crossref]
  • [54] AllixO., Ladeveze P., Corigliano A.,Damage analysis of interlaminarfracture specimens, Compos. Struct., 1995, 31(1), 61–74.[Crossref]
  • [55] Point N., Sacco E., A delamination model for laminated composites,Int. J. Solids Struct., 1996, 33(4), 483–509.[Crossref]
  • [56] Bolzon G., Corigliano A., A discrete formulation for elastic solidswith damaging interfaces, Comput. Meth. Appl. Mech. Eng.,1997, 140, 329–359.[Crossref]
  • [57] Allix O., Corigliano A., Geometrical and interfacial nonlinearitiesin the analysis of delamination in composites, Int. J.Solids Struct., 1999, 36(15), 2189–2216.[Crossref]
  • [58] Alfano G., Crisfield M.A., Finite element interface models forthe delamination analysis of laminated composites: mechanicaland computational issues, Int. J. Numer. Methods Eng., 2001,50, 1701–1736.[Crossref]
  • [59] Criesfield M.A., Alfano G., Adaptive hierarchical enrichment fordelamination fracture using a decohesive zone model, Int. J. Numer.Methods Eng., 2002, 54, 1369–1390.[Crossref]
  • [60] Guimatsia I., Ankersen J.K., Davies G.A.O., Iannucci L., Decohesionfinite element with enriched basis functions for delamination,Compos. Sci. Technol., 2009, 69(15-16), 2616–2624.[Crossref]
  • [61] Scott M.A., Borden M.J., Verhoosel C.V., Sederberg T.W., HughesT.J.R., Isogeometric finite element data structures based onBézier extraction of T-splines, Int. J. Numer. Methods Eng., 2011,88(2), 126–156.[Crossref]
  • [62] Scott M.A., Li X., Sederberg T.W., Hughes T.J.R., Local refinementof analysis-suitable T-splines, Comput. Meth. Appl. Mech. Eng.,2012, 213-216, 206–222.
  • [63] Li X., Zheng J., Sederberg T.W., Hughes T.J.R., Scott M.A., Onlinear independence of T-spline blending functions, Comput.Aided Geom. Des., 2012, 29(1), 63–76.[Crossref]
  • [64] Scott M.A., Simpson R.N., Evans J.A., Lipton S., Bordas S.P.A.,Hughes T.J.R., Sederberg T.W., Isogeometric boundary elementanalysis using unstructured T-splines, Comput. Meth. Appl.Mech. Eng., 2013, 254, 197–221.
  • [65] Giannelli C., Jüttler B., Speleers H., THB-splines: The truncatedbasis for hierarchical splines, Comput. Aided Geom. Des., 2012,29(7), 485–498.[Crossref]
  • [66] Deng J., Chen F., Li X., Hu C., Tong W., Yang Z., Feng Y., Polynomialsplines over hierarchical T-meshes, Graph. Models, 2008,70, 76–86.
  • [67] Dokken T., Lyche T., Pettersen K.F., Polynomial splines over locallyrefined box-partitions, Comput. Aided Geom. Des., 2013,30(3), 331–356.[Crossref]
  • [68] Dimitri R., De Lorenzis L., Wriggers P., Zavarise G., NURBS- andT-spline-based isogeoemtric cohesive zone modeling of interfacedebonding, Comput. Mech., 2014, 54, 369–388.[Crossref]
  • [69] Sederberg T.W., Zheng J., Bakenov A., Nasri A., T-splines and TNURCCSs,ACM T. Graphic., 2003, 22(3), 477–484.[Crossref]
  • [70] Sederberg T.W., Zheng J., Song X., Knot intervals and multidegreesplines, Comput. Aided Geom. Des., 2003, 20, 455–468.[Crossref]
  • [71] Sederberg T.W., Cardon D.L., Finnigan G.T., North N.S., ZhengJ., Lyche T., T-spline simplification and local refinement, ACM T.Graphic., 2004, 23 (3), 276–283.[Crossref]
  • [72] Cottrell J.A., Reali A., Bazilevs Y., Hughes T.J.R., Isogeometricanalysis of structural vibrations, Comput. Meth. Appl. Mech.Eng., 2006, 195, 5257–5296.[Crossref]
  • [73] Hughes T.J.R., Reali A., Sangalli G., Duality and unied analysis ofdiscrete approximations in structural dynamics and wave propagation:Comparison of p-method nite elements with k-methodNURBS, Comput. Meth. Appl. Mech. Eng., 2008, 197(49-50),4104–4124.[Crossref]
  • [74] Lorentz G. G., Bernstein Polynomials, Chelsea Publishing Co.,New York, 1986.
  • [75] Piegl L. A., Tiller W., The NURBS Book, Springer, 1996.
  • [76] Autodesk, 2011, Inc. http://www.tsplines.com/rhino/ .
  • [77] Schillinger D., Rank E., An unfitted hp-adaptive finite elementmethod based on hierarchical B-splines for interface problemsof complex geometry, Comput. Meth. Appl. Mech. Eng., 2011,200(47-48), 3358– 3380.[Crossref]
  • [78] Vuong A.V., Giannelli C., Jüttler B., Simeon B., A hierarchical approachto adaptive local refinement in isogeometric analysis,Comput. Meth. Appl. Mech. Eng., 2011, 49-52, 3554– 3567.
  • [79] Samet H., Foundations of Multidimensional and Metric DataStructures, Morgan Kaufmann Publishers: San Francisco, 2006.
  • [80] Burstedde C., Wilcox L.C., Ghattas O., p4est: Scalable Algorithmsfor Parallel Adaptive Mesh Refinement on Forests of Octrees,SIAM J. Sci. Comput., 2011, 33(3), 1103–1133.
  • [81] Yserantant H., On the multi-level splitting of finite elementspaces, Numer. Math., 1986, 49, 379–412.[Crossref]
  • [82] Krysl P., Grinspun E., Schröder P., Natural hierarchical refinementfor finite element methods, Int. J. Numer. Methods Eng.,2003, 56, 1109–1124.[Crossref]
  • [83] Bungartz H.J., Griebel M., Sparse grids, Acta Numer., 2004, 13,147–269.
  • [84] Taylor R.L., FEAP – Finite Element Analysis Program, 2013,www.ce.berkeley/feap, University of California, Berkeley.
  • [85] Laursen T.A., Computational contact and impact mechanics,2002, Springer, Berlin.
  • [86] P. Wriggers, Computational contact mechanics, 2nd edition,2006, Springer, Berlin.
  • [87] Puso M.A., Laursen T.A., A mortar segment-to-segment frictionalcontact method for large deformations, Comput. Meth.Appl. Mech. Eng., 2004, 193, 4891–4913.[Crossref]
  • [88] Papadopoulos P., Taylor R.L., A mixed formulation for the finiteelement solution of contact problems, Comput. Meth. Appl.Mech. Eng., 1992, 94(3), 373–389.[Crossref]
  • [89] Zienkiewicz O.C., Taylor R.L., The Finite Element Method forSolid and Structural Mechanics, 2005, Butterworth-Heinemann,6th edition.
  • [90] Kiendl J., Bletzinger K.U., Linhard J., Wüchner R., Isogeometricshell analysis with Kirchhoff-Love elements, Comput. Meth.Appl. Mech. Eng., 2009, 198(49-52), 3902–3914.[Crossref]
  • [91] Hermes F.H., Process zone and cohesive element size in numericalsimulations of delamination in bi-layers, Master thesis,September 24th 2010, MT 10.21, Eindhoven.
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