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Original Articles

Modeling of contact interfaces by penalty based enriched finite element method

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Pages 1485-1503 | Received 25 Oct 2021, Accepted 22 Jan 2022, Published online: 28 Feb 2022

References

  • A. Francavilla, and O. C. Zienkiewicz, A note on numerical computation of elastic contact problems, Int. J. Numer. Meth. Engng., vol. 9, no. 4, pp. 913–924, 1975. DOI: 10.1002/nme.1620090410.
  • T. D. Sachdeva, and C. V. Ramakrishnan, A finite element solution for the two‐dimensional elastic contact problems with friction, Int. J. Numer. Meth. Engng., vol. 17, no. 8, pp. 1257–1271, 1981. DOI: 10.1002/nme.1620170809.
  • R. P. Mechnik, Consideration of constraints within the finite element method by means of matrix operators, Int. J. Numer. Meth. Engng., vol. 31, no. 5, pp. 909–926, 1991. DOI: 10.1002/nme.1620310507.
  • C. Wen-Hwa, and Y. Jyi-Tyan, Finite element analysis of finite deformation contact problems with friction, Comput. Struct., vol. 29, no. 3, pp. 423–436, 1988. DOI: 10.1016/0045-7949(88)90395-1.
  • S. K. Arya, and G. A. Hegemier, Finite element method for interface problems, J. Struct. Div., vol. 108, no. 2, pp. 327–342, 1982. DOI: 10.1061/JSDEAG.0005874.
  • Osamu Doi, and Naoki Asano, Method for analysis of elasto-dynamic contact problems by finite element method, Bull. JSME., vol. 24, no. 189, pp. 528–533, 1981. DOI: 10.1299/jsme1958.24.528.
  • M. U. Rahman, R. E. Rowlands, R. D. Cook, and T. L. Wilkinson, An iterative procedure for finite-element stress analysis of frictional contact problems, Comput. Struct., vol. 18, no. 6, pp. 947–954, 1984. DOI: 10.1016/0045-7949(84)90138-X.
  • T. J. R. Hughes, R. L. Taylor, J. L. Sackman, A. Curnier, and W. Kanoknukulchai, A finite element method for a class of contact-impact problems, Comput. Methods Appl. Mech. Eng., vol. 8, no. 3, pp. 249–276, 1976. DOI: 10.1016/0045-7825(76)90018-9.
  • A. B. Chaudhary, and K. J. Bathe, A solution method for static and dynamic analysis of three-dimensional contact problems with friction, Comput. Struct., vol. 24, no. 6, pp. 855–873, 1986. DOI: 10.1016/0045-7949(86)90294-4.
  • J. C. Simo, P. Wriggers, and R. L. Taylor, A perturbed Lagrangian formulation for the finite element solution of contact problems, Comput. Methods Appl. Mech. Eng., vol. 50, no. 2, pp. 163–180, 1985. DOI: 10.1016/0045-7825(85)90088-X.
  • F. J. Gallego, and J. J. Anza, A mixed finite element model for the elastic contact problem, Int. J. Numer. Meth. Engng., vol. 28, no. 6, pp. 1249–1264, 1989. DOI: 10.1002/nme.1620280603.
  • Y. Kanto, and G. Yagawa, A dynamic contact buckling analysis by the penalty finite element method, Int. J. Numer. Meth. Engng., vol. 29, no. 4, pp. 755–774, 1990. DOI: 10.1002/nme.1620290406.
  • D. Perić, and D. R. J. Owen, Computational model for 3‐D contact problems with friction based on the penalty method, Int. J. Numer. Meth. Engng., vol. 35, no. 6, pp. 1289–1309, 1992. DOI: 10.1002/nme.1620350609.
  • A. R. Khoei, and M. Nikbakht, An enriched finite element algorithm for numerical computation of contact friction problems, Int. J. Mech. Sci., vol. 49, no. 2, pp. 183–199, 2007. DOI: 10.1016/j.ijmecsci.2006.08.014.
  • W. Zhong, Parametric variational principle and parametric quadratic programming method for elastic contact problem, Comput Struct Mech Appl., vol. 2, pp. 1–9, 1985.
  • A. Klarbring, A mathematical programming approach to three-dimensional contact problems with friction, Comput. Methods Appl. Mech. Eng., vol. 58, no. 2, pp. 175–200, 1986. DOI: 10.1016/0045-7825(86)90095-2.
  • S. Hartmann, S. Brunssen, E. Ramm, and B. Wohlmuth, Unilateral non-linear dynamic contact of thin-walled structures using a primal-dual active set strategy, Int. J. Numer. Meth. Engng., vol. 70, no. 8, pp. 883–912, 2007. DOI: 10.1002/nme.1894.
  • J. Haslinger, Z. Dostál, and R. Kučera, On a splitting type algorithm for the numerical realization of contact problems with Coulomb friction, Comput. Methods Appl. Mech. Eng., vol. 191, no. 21–22, pp. 2261–2281, 2002. DOI: 10.1016/S0045-7825(01)00378-4.
  • J. Haslinger, V. Janovský, and T. Ligurský, Qualitative analysis of solutions to discrete static contact problems with Coulomb friction, Comput. Methods Appl. Mech. Eng., vol. 205–208, pp. 149–161, 2012. DOI: 10.1016/j.cma.2010.09.010.
  • Z. Q. Xie, H. W. Zhang, and B. S. Chen, A finite element model for 3D frictional contact analysis of Cosserat materials, Finite Elem. Anal. Des., vol. 57, pp. 92–102, 2012. DOI: 10.1016/j.finel.2012.03.009.
  • P. Laborde, and Y. Renard, Fixed point strategies for elastostatic factional contact problems, Math. Meth. Appl. Sci., vol. 31, no. 4, pp. 415–441, 2008. DOI: 10.1002/mma.921.
  • P. Wriggers, J. Schröder, and A. Schwarz, A finite element method for contact using a third medium, Comput. Mech., vol. 52, no. 4, pp. 837–847, 2013. DOI: 10.1007/s00466-013-0848-5.
  • N. Vu-Bac, et al., A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics, J. Appl. Math., vol. 2013, pp. 1–12, 2013. DOI: 10.1155/2013/978026.
  • P. Broumand, and A. R. Khoei, General framework for dynamic large deformation contact problems based on phantom-node X-FEM, Comput. Mech., vol. 61, no. 4, pp. 449–469, 2018. DOI: 10.1007/s00466-017-1463-7.
  • T. Belytschko, and T. Black, Elastic crack growth in finite elements with minimal remeshing, Int. J. Numer. Meth. Engng., vol. 45, no. 5, pp. 601–620, 1999. DOI: 10.1002/(SICI)1097-0207(19990620)45:5 < 601::AID-NME598 > 3.0.CO;2-S.
  • Nicolas MoëS, John Dolbow, and Ted Belytschko, A finite element method for crack growth without remeshing, Int. J. Numer. Meth. Engng., vol. 46, no. 1, pp. 131–150, 1999. DOI: 10.1002/(sici)1097-0207(19990910)46:1 < 131::aid-nme726 > 3.3.co;2-a.
  • A. Jameel, and G. A. Harmain, Effect of material irregularities on fatigue crack growth by enriched techniques, Int. J. Comput. Methods Eng. Sci. Mech., vol. 21, no. 3, pp. 109–133, 2020. DOI: 10.1080/15502287.2020.1772902.
  • S. A. Kanth, A. S. Lone, G. A. Harmain, and A. Jameel, Modeling of embedded and edge cracks in steel alloys by XFEM, Mater. Today Proc., vol. 26, pp. 814–818, 2020. DOI: 10.1016/j.matpr.2019.12.423.
  • T. Rabczuk, and T. Belytschko, Cracking particles: A simplified meshfree method for arbitrary evolving cracks, Int. J. Numer. Meth. Engng., vol. 61, no. 13, pp. 2316–2343, 2004. DOI: 10.1002/nme.1151.
  • A. Jameel, and G. A. Harmain, Fatigue crack growth in presence of material discontinuities by EFGM, Int. J. Fatigue., vol. 81, pp. 105–116, 2015. DOI: 10.1016/j.ijfatigue.2015.07.021.
  • A. Jameel, and G. A. Harmain, Fatigue crack growth analysis of cracked specimens by the coupled finite element-element free Galerkin method, Mech. Adv. Mater. Struct., vol. 26, no. 16, pp. 1343–1356, 2019. DOI: 10.1080/15376494.2018.1432800.
  • T. J. R. Hughes, J. A. Cottrell, and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Eng., vol. 194, no. 39-41, pp. 4135–4195, 2005. DOI: 10.1016/j.cma.2004.10.008.
  • R. Kruse, N. Nguyen-Thanh, P. Wriggers, and LDe Lorenzis, Isogeometric frictionless contact analysis with the third medium method, Comput. Mech., vol. 62, no. 5, pp. 1009–1021, 2018. DOI: 10.1007/s00466-018-1547-z.
  • A. Jameel, and G. A. Harmain, A coupled FE-IGA technique for modeling fatigue crack growth in engineering materials, Mech. Adv. Mater. Struct., vol. 26, no. 21, pp. 1764–1775, 2019. DOI: 10.1080/15376494.2018.1446571.
  • A. Jameel, and G. A. Harmain, Extended iso-geometric analysis for modeling three-dimensional cracks, Mech. Adv. Mater. Struct., vol. 26, no. 11, pp. 915–923, 2019. DOI: 10.1080/15376494.2018.1430275.
  • A. Jameel, and G. A. Harmain, Large deformation in bi-material components by XIGA and coupled FE-IGA techniques, Mech. Adv. Mater. Struct., pp. 1–23, 2020. DOI: 10.1080/15376494.2020.1799120.
  • I. V. Singh, B. K. Mishra, and S. Bhattacharya, XFEM simulation of cracks, holes and inclusions in functionally graded materials, Int. J. Mech. Mater. Des., vol. 7, no. 3, pp. 199–218, 2011. DOI: 10.1007/s10999-011-9159-1.
  • S. Bordas, and B. Moran, Enriched finite elements and level sets for damage tolerance assessment of complex structures, Eng. Fract. Mech., vol. 73, no. 9, pp. 1176–1201, 2006. DOI: 10.1016/j.engfracmech.2006.01.006.
  • V. B. Pandey, I. V. Singh, B. K. Mishra, S. Ahmad, A. Venugopal Rao, and V. Kumar, A new framework based on continuum damage mechanics and XFEM for high cycle fatigue crack growth simulations, Eng. Fract. Mech., vol. 206, 172–200, 2019. DOI: 10.1016/j.engfracmech.2018.11.021..
  • M. Bansal, I. V. Singh, R. U. Patil, S. Claus, and S. P. A. Bordas, A simple and robust computational homogenization approach for heterogeneous particulate composites, Comput. Methods Appl. Mech. Eng., vol. 349, 45–90, 2019. DOI: 10.1016/j.cma.2019.02.001..
  • N. Duhan, R. U. Patil, B. K. Mishra, I. V. Singh, and Y. E. Pak, Thermo-elastic analysis of edge dislocation using extended finite element method, Int. J. Mech. Sci., vol. 192, pp. 106109, 2021. DOI: 10.1016/j.ijmecsci.2020.106109.
  • J. M. Melenk, and I. Babuška, The partition of unity finite element method: Basic theory and applications, Comput. Methods Appl. Mech. Eng., vol. 139, no. 1–4, pp. 289–314, 1996. DOI: 10.1016/S0045-7825(96)01087-0.
  • I. Babuška, and J. M. Melenk, The partition of unity method, Int. J. Numer. Meth. Engng., vol. 40, no. 4, pp. 727–758, 1997. DOI: 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N.
  • M. Stolarska, D. L. Chopp, N. Mos, and T. Belytschko, Modelling crack growth by level sets in the extended finite element method, Int. J. Numer. Meth. Engng., vol. 51, no. 8, pp. 943–960, 2001. DOI: 10.1002/nme.201.
  • T. Belytschko, N. Moës, S. Usui, and C. Parimi, Arbitrary discontinuities in finite elements, Int. J. Numer. Meth. Engng., vol. 50, no. 4, pp. 993–1013, 2001. DOI: 10.1002/1097-0207(20010210)50:4<993::AID-NME164>3.0.CO;2-M.
  • N. Sukumar, D. L. Chopp, N. Moës, and T. Belytschko, Modeling holes and inclusions by level sets in the extended finite-element method, Comput. Methods Appl. Mech. Eng., vol. 190, no. 46–47, pp. 6183–6200, 2001. DOI: 10.1016/S0045-7825(01)00215-8.
  • S. Kumar, I. V. Singh, B. K. Mishra, K. Sharma, and I. A. Khan, A homogenized multigrid XFEM to predict the crack growth behavior of ductile material in the presence of microstructural defects, Eng. Fract. Mech., vol. 205, 2019. DOI: 10.1016/j.engfracmech.2016.03.051.
  • M. Kumar, I. V. Singh, and B. K. Mishra, Fatigue crack growth simulations of plastically graded materials using XFEM and J-integral decomposition approach, Eng. Fract. Mech., vol. 216 (106470), pp. 1–24, 2019. DOI: 10.1016/j.engfracmech.2019.05.002.
  • M. Kumar, and I. V. Singh, Numerical investigation of creep crack growth in plastically graded materials using C(t) and XFEM, Eng. Fract. Mech., vol. 226, pp. 106820, 2020. DOI: 10.1016/j.engfracmech.2019.106820.
  • V. B. Pandey, I. V. Singh, B. K. Mishra, S. Ahmad, A. V. Rao, and V. Kumar, Creep crack simulations using continuum damage mechanics and extended finite element method, Int. J. Damage Mech., vol. 28, no. 1, pp. 3–34, 2019. DOI: 10.1177/1056789517737593.
  • J. Jena, S. K. Singh, V. Gaur, I. V. Singh, and S. Natarajan, A new framework based on XFEM for cracked semipermeable piezoelectric material, Eng. Fract. Mech., vol. 253, pp. 107874, 2021. DOI: 10.1016/j.engfracmech.2021.107874.
  • A. S. Lone, S. A. Kanth, A. Jameel, and G. A. Harmain, A state of art review on the modeling of contact type nonlinearities by extended finite element method, Mater, Today Proc., vol. 18, pp. 3462–3471, 2019. DOI: 10.1016/j.matpr.2019.07.274.
  • A. R. Khoei, and M. Nikbakht, Contact friction modeling with the extended finite element method (X-FEM), J. Mater. Process. Technol., vol. 177, no. 1, pp. 58–62, 2006. DOI: 10.1016/j.jmatprotec.2006.03.185.
  • M. Siavelis, P. Massin, M. L. E. Guiton, S. Mazet, and N. Moës, Robust implementation of contact under friction and large sliding with the eXtended finite element method, Eur. J. Comput. Mech., vol. 19, no. 1–3, pp. 189–203, 2010. DOI: 10.3166/ejcm.19.189-203.
  • I. Nistor, M. L. E. Guiton, P. Massin, N. Moës, and S. Géniaut, An X-FEM approach for large sliding contact along discontinuities, Int. J. Numer. Methods Eng., vol. 78, no. 12, 1407–1435, 2009. DOI: 10.1002/nme.2532..
  • M. Siavelis, M. L. E. Guiton, P. Massin, and N. Moës, Large sliding contact along branched discontinuities with X-FEM, Comput. Mech., vol. 52, no. 1, pp. 201–219, 2013. DOI: 10.1007/s00466-012-0807-6.
  • A. S. Shedbale, A. K. Sharma, I. V. Singh, and B. K. Mishra, Modeling and simulation of metal forming processes by XFEM, Amm., vol. 829, pp. 41–45, 2016. DOI: 10.4028/www.scientific.net/AMM.829.41.
  • A. S. Lone, S. A. Kanth, G. A. Harmain, and A. Jameel, XFEM modeling of frictional contact between elliptical inclusions and solid bodies, Mater. Today Proc., vol. 26, pp. 819–824, 2020. DOI: 10.1016/j.matpr.2019.12.424.
  • F. Parrinello, and G. Marannano, 1 Dipartimento di Ingegneria Civile Ambientale Aerospaziale e dei Materiali, Universitá of Palermo, Viale delle Scienza, 90128 Palermo, Italy Cohesive delamination and frictional contact on joining surface via XFEM, AIMS Mater. Sci., vol. 5, no. 1, pp. 127–144, 2018. DOI: 10.3934/matersci.2018.1.127.
  • M. Paggi, and P. Wriggers, Node-to-segment and node-to-surface interface finite elements for fracture mechanics, Comput. Methods Appl. Mech. Eng., vol. 300, pp. 540–560, 2016. DOI: 10.1016/j.cma.2015.11.023.
  • A. S. Lone, A. Jameel, and G. A. Harmain, A coupled finite element-element free Galerkin approach for modeling frictional contact in engineering components, In: Mater. Today Proc., vol. 5, no. 9, pp. 18745–18754, 2018. DOI: 10.1016/j.matpr.2018.06.221.
  • V. P. Nguyen, C. T. Nguyen, S. Bordas, and A. Heidarpour, Modelling interfacial cracking with non-matching cohesive interface elements, Comput. Mech., vol. 58, no. 5, pp. 731–746, 2016. DOI: 10.1007/s00466-016-1314-y.
  • T. Y. Kim, J. Dolbow, and T. Laursen, A mortared finite element method for frictional contact on arbitrary interfaces, Comput. Mech., vol. 39, no. 3, pp. 223–235, 2006. DOI: 10.1007/s00466-005-0019-4.
  • F. Liu, and R. I. Borja, A contact algorithm for frictional crack propagation with the extended finite element method, Int. J. Numer. Meth. Engng., vol. 76, no. 10, pp. 1489–1512, 2008. DOI: 10.1002/nme.2376.
  • J. T. Oden, and J. A. C. Martins, Models and computational methods for dynamic friction phenomena, Comput. Methods Appl. Mech. Eng., vol. 52, no. 1–3, pp. 527–634, 1985. DOI: 10.1016/0045-7825(85)90009-X.
  • P. Alart, and A. Curnier, A mixed formulation for frictional contact problems prone to Newton like solution methods, Comput. Methods Appl. Mech. Eng., vol. 92, no. 3, pp. 353–375, 1991. DOI: 10.1016/0045-7825(91)90022-X.
  • S. Stupkiewicz, Extension of the node-to-segment contact element for surface-expansion-dependent contact laws, Int. J. Numer. Meth. Engng., vol. 50, no. 3, pp. 739–759, 2001. DOI: 10.1002/1097-0207(20010130)50:3<739::AID-NME49>3.0.CO;2-G.
  • A. E. Giannakopoulos, The return mapping method for the integration of friction constitutive relations, Comput. Struct., vol. 32, no. 1, pp. 157–167, 1989. DOI: 10.1016/0045-7949(89)90081-3.
  • A. R. Khoei, S. Keshavarz, and A. R. Khaloo, Modeling of large deformation frictional contact in powder compaction processes, Appl. Math. Model., vol. 32, no. 5, pp. 775–801, 2008. DOI: 10.1016/j.apm.2007.02.017.
  • A. R. Khoei, S. O. R. Biabanaki, and M. Anahid, A Lagrangian-extended finite-element method in modeling large-plasticity deformations and contact problems, Int. J. Mech. Sci., vol. 51, no. 5, pp. 384–401, 2009. DOI: 10.1016/j.ijmecsci.2009.03.012.
  • K. L. Johnson, Contact Mechanics., vol. 37, pp. 29–43, 1989. DOI: 10.1201/b17110-2.

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