Abstract
Nowadays the isogeometric analysis (IGA) represents an innovative method that merges design and numerical computations into a unified formulation. In such a context we apply the isogeometric concept based on T-splines and Non Uniform Rational B-Splines (NURBS) discretizations to study the interfacial contact and debonding problems between deformable bodies in large deformations. More in detail, we develop and test a generalized large deformation contact algorithm which accounts for both frictional contact and mixed-mode cohesive debonding in a unified setting. Some numerical examples are provided for varying resolutions of the contact and/or cohesive zone, which show the accuracy of the solutions and demonstrate the potential of the method to solve challenging 2D contact and debonding problems. The superior accuracy of T-splines with respect to NURBS interpolations for a given number of degrees of freedom (Dofs) is always proved.
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References
Puso MA, Laursen TA, Solberg J (2008) A segment-to-segment mortar contact method for quadratic elements and large deformations. Comput Methods Appl Mech Eng 197:555–566
Franke D, Düster A, Nübel V, Rank E (2010) A comparison of the h-, p-, hp- and rp-version of the FEM for the solution of the 2D Hertzian contact problem. Comput Mech 45:513–522
De Lorenzis L, Temizer I, Wriggers P, Zavarise G (2011) A large deformation frictional contact formulation using NURBS-based isogeometric analysis. Int J Numer Methods Eng 87(13):1278–1300
De Lorenzis L, Wriggers P, Zavarise G (2012) A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method. Comput Mech 49(1):1–20
Temizer I, Wriggers P, Hughes TJR (2011) Contact treatment in isogeometric analysis with NURBS. Comput Methods Appl Mech Eng 200:1100–1112
Temizer I, Wriggers P, Hughes TJR (2012) Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS. Comput Methods Appl Mech Eng 209:115–128
Corbett CJ, Sauer R (2014) NURBS-enriched contact finite elements. Comput Methods Appl Mech Eng 275:55–75
Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195
Scott MA, Simpson RN, Evans JA, Lipton S, Bordas SPA, Hughes TJR, Sederberg TW (2013) Isogeometric boundary element analysis using unstructured T-splines. Comput Methods Appl Mech Eng 254:197–221
Bazilevs Y, Calo VM, Cottrell JA, Evans JA, Hughes TJR, Lipton S, Scottand MA, Sederberg TW (2010) Isogeometric analysis using T-splines. Comput Methods Appl Mech Eng 199:229–263
Dörfel M, Juttler B, Simeon B (2010) Adaptive isogeometric analysis by local h-refinement with T-splines. Comput Methods Appl Mech Eng 199:264–275
Nguyen-Thanh N, Nguyen-Xuan H, Bordas S, Rabczuk T (2011) Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids. Comput Methods Appl Mech Eng 200(21–22):1892–1908
Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, Wü uchner R, Bletzinger KU, Bazilevs Y, Rabczuk T (2011) Rotation free isogeometric thin shell analysis using PHT-splines. Comput Methods Appl Mech Eng 200(47–48):3410–3424
Nguyen-Thanh N, Muthu J, Zhuang X, Rabczuk T (2013) An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics. Comput Mech 53:369–385
Schillinger D, Dede L, Scott MA, Evans JA, Borden MJ, Rank E, Hughes TJR (2012) An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces. Comput Methods Appl Mech Eng 249–252:116–150
Vuong A-V, Giannelli C, Jüttler B, Simeon B (2012) A hierarchical approach to adaptive local refinement in isogeometric analysis. Comput Methods Appl Mech Eng 200:3554–3567
Dimitri R, De Lorenzis L, Scott M, Wriggers P, Taylor RL, Zavarise G (2014) Isogeometric large deformation frictionless contact using T-splines. Comput Methods Appl Mech Eng 269:394–414
Taylor RL (2013) FEAP—finite element analysis program, University of California, Berkeley. www.ce.berkeley/feap
Alfano G, Crisfield MA (2001) Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. Int J Numer Methods Eng 50:1701–1736
Xu XP, Needleman A (1993) Void nucleation by inclusions debonding in a crystal matrix. Model Simul Mater Sci Eng 1:111–132
van den Bosch MJ, Schreurs PJG, Geers MGD (2006) An improved description of the exponential Xu and Needleman cohesive zone law for mixed-mode decohesion. Eng Fract Mech 73:1220–1234
Dimitri R, Trullo M, De Lorenzis L, Zavarise G (2015) Coupled cohesive zone models for mixed-mode fracture: a comparative study. Eng Fract Mech 148:145–179
ASTM D 6671/D 6671M (2006). Standard test method for mixed mode I-mode II interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites
ASTM D 3165-07 (2014). Standard test method for strength properties of adhesives in shear by tension loading of single-lap joint laminated assemblies
Hughes TJR (1987) The finite element method. Linear static and dynamic finite element analysis. Prentice-hall, Englewood Cliffs
Scott MA, Li X, Sederberg TW, Hughes TJR (2012) Local refinement of analysis-suitable T-splines. Comput Methods Appl Mech Eng 213–216:206–222
Vuong AV, Giannelli C, Juttler B, Simeon B (2011) A hierarchical approach to adaptive local refinement in isogeometric analysis. Comput Methods Appl Mech Eng 200:3554–3567
Schillinger D, Dedè L, Scott MA, Evans JA, Borden MJ, Rank E, Hughes TJR (2012) An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces. Comput Methods Appl Mech Eng 249–250:116–150
Scott MA, Thomas DC, Evans EJ (2014) Isogeometric spline forests. Comput Methods Appl Mech Eng 269:222–264
Dimitri R, De Lorenzis L, Wriggers P, Zavarise G (2014) NURBS- and T-spline-based isogeometric cohesive zone modeling of interface debonding. Comput Mech 54:369–388
Scott MA, Borden MJ, Verhoosel CV, Sederberg TW, Hughes TJR (2011) Isogeometric finite element data structures based on Bézier extraction of Tsplines. Numer Methods Eng 88(2):126–156
Sederberg TW, Zheng J, Bakenov A, Nasri A (2003) T-splines and T-NURCCSs. ACM Trans Graph 22(3):477–484
Sederberg TW, Cardon DL, Finnigan GT, North NS, Zheng J, Lyche T (2004) T-spline simplification and local refinement. ACM Trans Graph 23(3):276–283
Laursen TA (2002) Computational contact and impact mechanics. Springer, Berlin
Wriggers P (2006) Computational contact mechanics, 2nd edn. Springer, Berlin
Zavarise G, Boso D, Scherefler BA (2001) A contact formulation for electrical and mechanical resistance. In: Martins JAC, Monteiro Marques MDP (eds) Proceedings of CMIS III, contact mechanics international symposium, Praja de Consolacao, Protugal, pp 211–218
Autodesk, Inc. (2011). http://www.tsplines.com/rhino/
Nowell D, Hills DA, Sackfield A (1988) Contact of dissimilar elastic cylinders under normal and tangential loading. J Mech Phys Solids 36(1):59–75
Hills DA, Nowell D (1994) Mechanics of fretting fatigue. Kluwer Academic Publishers, Dordrecht
Reeder JR, Crews JrJH (1990) Mixed-mode bending method for delamination testing. AIAA J 28(7):1270–1276
Mi Y, Crisfield MA (1996) Analytical derivation of load/displacement relationships for mixed-mode delamination and comparison with finite element results. Imperial college, Department of Aeronautics, London
Galietti U, Dimitri R, Palumbo D, Rubino P (2012) Thermal analysis and mechanical characterization of GFRP joints. In: ECCM15, 15th European conference on composite materials
Acknowledgements
The first author would like to acknowledge the Regional progject “MIPER PS_095 (Innovative Materials and Methodologies for Products in Renewable Energy sector), and the ENEA Research Centre of Brindisi (UTTMATB-COMP) where the experimental investigation on the composite adhesive joints has been performed.
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Dimitri, R., Zavarise, G. Isogeometric treatment of frictional contact and mixed mode debonding problems. Comput Mech 60, 315–332 (2017). https://doi.org/10.1007/s00466-017-1410-7
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DOI: https://doi.org/10.1007/s00466-017-1410-7