The Effect of Inclusion on Crack Propagation Using Extended Finite Element Method
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Keywords
Crack propagation, XFEM, Level set, Inclusion
Abstract
Numerical simulation is developed to investigate the effect of inclusion on crack propagation. In this study, the crack growth is modeled using extended finite element method (XFEM). Two-dimensional rectangular plate with single inclusion embedded off-centered is modeled. The specimen is subjected to uniaxial tension. The dimensions of the specimen are 40 mm x 80 mm and the radius of the inclusion is 10 mm. The specimen is pre-cracked with the length of an edge crack is 5 mm. The motion of the crack is modeled by XFEM based on traction-separation cohesive behavior for 2D mixed mode problem. In addition, enrichment procedure is used to implicitly determine predefined crack in XFEM framework. Two different inclusions, which are soft and hard inclusions, are considered on crack propagation scheme. The effects of soft and hard inclusions on crack propagation are studied and observed. The results showed that the trajectory of crack highly depends on inclusion inside the material. In the case of soft inclusion, propagation of the crack tended to approach the inclusion. Whereas in the case of hard inclusion, crack trajectory tended to move away from the inclusion. The mismatch of elastic modulus between inclusion and surrounded materials has significant effect on propagation of crack.
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[2] T. Rabczuk and T. Belytschko, “Cracking particles: A simplified meshfree method for arbitrary evolving cracks,” Int. J. Numer. Methods Eng., vol. 61, no. 13, pp. 2316–2343, 2004, doi: 10.1002/nme.1151.
[3] T. Rabczuk and T. Belytschko, “A three-dimensional large deformation meshfree method for arbitrary evolving cracks,” Comput. Methods Appl. Mech. Eng., vol. 196, no. 29–30, pp. 2777–2799, 2007, doi: 10.1016/j.cma.2006.06.020.
[4] T. Rabczuk and G. Zi, “A meshfree method based on the local partition of unity for cohesive cracks,” Comput. Mech., vol. 39, no. 6, pp. 743–760, 2007, doi: 10.1007/s00466-006-0067-4.
[5] P. M. A. Areias and T. Rabczuk, “Quasi-static crack propagation in plane and plate structures using set-valued traction-separation laws,” Int. J. Numer. Methods Eng., vol. 74, no. 3, pp. 475–505, 2008, doi: 10.1002/nme.2182.
[6] L. Chen, T. Rabczuk, S. P. A. Bordas, G. R. Liu, K. Y. Zeng, and P. Kerfriden, “Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth,” Comput. Methods Appl. Mech. Eng., vol. 209–212, pp. 250–265, 2012, doi: 10.1016/j.cma.2011.08.013.
[7] H. Nguyen-Vinh et al., “Extended finite element method for dynamic fracture of piezo-electric materials,” Eng. Fract. Mech., vol. 92, pp. 19–31, 2012, doi: 10.1016/j.engfracmech.2012.04.025.
[8] C. Zhang, C. Wang, T. Lahmer, P. He, and T. Rabczuk, “A dynamic XFEM formulation for crack identification,” Int. J. Mech. Mater. Des., vol. 12, no. 4, pp. 427–448, 2016, doi: 10.1007/s10999-015-9312-3.
[9] N. Vu-Bac et al., “A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis,” C. - Comput. Model. Eng. Sci., vol. 73, no. 4, pp. 331–355, 2011.
[10] F. Amiri, D. Millán, Y. Shen, T. Rabczuk, and M. Arroyo, “Phase-field modeling of fracture in linear thin shells,” Theor. Appl. Fract. Mech., vol. 69, pp. 102–109, 2014, doi: 10.1016/j.tafmec.2013.12.002.
[11] F. Amiri, C. Anitescu, M. Arroyo, S. P. A. Bordas, and T. Rabczuk, “XLME interpolants, a seamless bridge between XFEM and enriched meshless methods,” Comput. Mech., vol. 53, no. 1, pp. 45–57, 2014, doi: 10.1007/s00466-013-0891-2.
[12] Y. L. Gui, H. H. Bui, J. Kodikara, Q. B. Zhang, J. Zhao, and T. Rabczuk, “Modelling the dynamic failure of brittle rocks using a hybrid continuum-discrete element method with a mixed-mode cohesive fracture model,” Int. J. Impact Eng., vol. 87, pp. 146–155, 2016, doi: 10.1016/j.ijimpeng.2015.04.010.
[13] V. P. Nguyen, H. Lian, T. Rabczuk, and S. Bordas, “Modelling hydraulic fractures in porous media using flow cohesive interface elements,” Eng. Geol., vol. 225, pp. 68–82, 2017, doi: 10.1016/j.enggeo.2017.04.010.
[14] P. Areias, T. Rabczuk, and D. Dias-da-Costa, “Element-wise fracture algorithm based on rotation of edges,” Eng. Fract. Mech., vol. 110, pp. 113–137, 2013, doi: 10.1016/j.engfracmech.2013.06.006.
[15] P. Areias and T. Rabczuk, “Finite strain fracture of plates and shells with configurational forces and edge rotations,” Int. J. Numer. Methods Eng., vol. 94, no. 12, pp. 1099–1122, 2013, doi: 10.1002/nme.4477.
[16] P. Areias, T. Rabczuk, and P. P. Camanho, “Finite strain fracture of 2D problems with injected anisotropic softening elements,” Theor. Appl. Fract. Mech., vol. 72, no. 1, pp. 50–63, 2014, doi: 10.1016/j.tafmec.2014.06.006.
[17] P. Areias, T. Rabczuk, and M. A. Msekh, “Phase-field analysis of finite-strain plates and shells including element subdivision,” Comput. Methods Appl. Mech. Eng., vol. 312, pp. 322–350, 2016, doi: 10.1016/j.cma.2016.01.020.
[18] P. Areias, M. A. Msekh, and T. Rabczuk, “Damage and fracture algorithm using the screened Poisson equation and local remeshing,” Eng. Fract. Mech., vol. 158, pp. 116–143, 2016, doi: 10.1016/j.engfracmech.2015.10.042.
[19] P. Areias and T. Rabczuk, “Steiner-point free edge cutting of tetrahedral meshes with applications in fracture,” Finite Elem. Anal. Des., vol. 132, pp. 27–41, 2017, doi: 10.1016/j.finel.2017.05.001.
[20] H. Ren, X. Zhuang, Y. Cai, and T. Rabczuk, “Dual-horizon peridynamics,” Int. J. Numer. Methods Eng., vol. 108, no. 12, pp. 1451–1476, 2016, doi: 10.1002/nme.5257.
[21] H. Ren, X. Zhuang, and T. Rabczuk, “Dual-horizon peridynamics: A stable solution to varying horizons,” Comput. Methods Appl. Mech. Eng., vol. 318, pp. 762–782, 2017, doi: 10.1016/j.cma.2016.12.031.
[22] K. M. Hamdia, T. Lahmer, T. Nguyen-Thoi, and T. Rabczuk, “Predicting the fracture toughness of PNCs: A stochastic approach based on ANN and ANFIS,” Comput. Mater. Sci., vol. 102, pp. 304–313, 2015, doi: 10.1016/j.commatsci.2015.02.045.
[23] K. M. Hamdia, X. Zhuang, P. He, and T. Rabczuk, “Fracture toughness of polymeric particle nanocomposites: Evaluation of models performance using Bayesian method,” Compos. Sci. Technol., vol. 126, pp. 122–129, 2016, doi: 10.1016/j.compscitech.2016.02.012.
[24] H. Talebi, M. Silani, S. P. A. Bordas, P. Kerfriden, and T. Rabczuk, “A computational library for multiscale modeling of material failure,” Comput. Mech., vol. 53, no. 5, pp. 1047–1071, 2014, doi: 10.1007/s00466-013-0948-2.
[25] H. Talebi, M. Silani, and T. Rabczuk, “Concurrent multiscale modeling of three dimensional crack and dislocation propagation,” Adv. Eng. Softw., vol. 80, no. C, pp. 82–92, 2015, doi: 10.1016/j.advengsoft.2014.09.016.
[26] P. R. Budarapu, R. Gracie, S. P. A. Bordas, and T. Rabczuk, “An adaptive multiscale method for quasi-static crack growth,” Comput. Mech., vol. 53, no. 6, pp. 1129–1148, 2014, doi: 10.1007/s00466-013-0952-6.
[27] S. W. Yang, P. R. Budarapu, D. R. Mahapatra, S. P. A. Bordas, G. Zi, and T. Rabczuk, “A meshless adaptive multiscale method for fracture,” Comput. Mater. Sci., vol. 96, no. PB, pp. 382–395, 2015, doi: 10.1016/j.commatsci.2014.08.054.
[28] P. R. Budarapu, R. Gracie, S. W. Yang, X. Zhuang, and T. Rabczuk, “Efficient coarse graining in multiscale modeling of fracture,” Theor. Appl. Fract. Mech., vol. 69, pp. 126–143, 2014, doi: 10.1016/j.tafmec.2013.12.004.
[29] B. Arash, H. S. Park, and T. Rabczuk, “Tensile fracture behavior of short carbon nanotube reinforced polymer composites: A coarse-grained model,” Compos. Struct., vol. 134, pp. 981–988, 2015, doi: 10.1016/j.compstruct.2015.09.001.
[30] B. Arash, H. S. Park, and T. Rabczuk, “Coarse-grained model of the J-integral of carbon nanotube reinforced polymer composites,” Carbon N. Y., vol. 96, pp. 1084–1092, 2016, doi: 10.1016/j.carbon.2015.10.058.
[31] T. Rabczuk, G. Zi, S. Bordas, and H. Nguyen-Xuan, “A simple and robust three-dimensional cracking-particle method without enrichment,” Comput. Methods Appl. Mech. Eng., vol. 199, no. 37–40, pp. 2437–2455, 2010, doi: 10.1016/j.cma.2010.03.031.
[32] T. Rabczuk, R. Gracie, J. H. Song, and T. Belytschko, “Immersed particle method for fluid-structure interaction,” Int. J. Numer. Methods Eng., vol. 81, no. 1, pp. 48–71, 2010, doi: 10.1002/nme.2670.
[33] T. Rabczuk, J. H. Song, and T. Belytschko, “Simulations of instability in dynamic fracture by the cracking particles method,” Eng. Fract. Mech., vol. 76, no. 6, pp. 730–741, 2009, doi: 10.1016/j.engfracmech.2008.06.002.
[34] T. Rabczuk, G. Zi, S. Bordas, and H. Nguyen-Xuan, “A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures,” Eng. Fract. Mech., vol. 75, no. 16, pp. 4740–4758, 2008, doi: 10.1016/j.engfracmech.2008.06.019.
[35] T. Rabczuk, G. Zi, A. Gerstenberger, and W. A. Wall, “A new crack tip element for the phantom-node method with arbitrary cohesive cracks,” Int. J. Numer. Methods Eng., vol. 75, no. 5, pp. 577–599, 2008, doi: 10.1002/nme.2273.
[36] T. Rabczuk and E. Samaniego, “Discontinuous modelling of shear bands using adaptive meshfree methods,” Comput. Methods Appl. Mech. Eng., vol. 197, no. 6–8, pp. 641–658, 2008, doi: 10.1016/j.cma.2007.08.027.
[37] T. Rabczuk, P. M. A. Areias, and T. Belytschko, “A meshfree thin shell method for non-linear dynamic fracture,” Int. J. Numer. Methods Eng., vol. 72, no. 5, pp. 524–548, 2007, doi: 10.1002/nme.2013.
[38] T. Rabczuk, S. Bordas, and G. Zi, “A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics,” Comput. Mech., vol. 40, no. 3, pp. 473–495, 2007, doi: 10.1007/s00466-006-0122-1.
[39] T. Belytscho, Y. Y. Lu, and L. Gu, “Element-free galerkin methods, International Journal for Numerical Methods in Engineering,” 1994.
[40] V. P. Nguyen, T. Rabczuk, S. Bordas, and M. Duflot, “Meshless methods: A review and computer implementation aspects,” Math. Comput. Simul., vol. 79, no. 3, pp. 763–813, 2008, doi: 10.1016/j.matcom.2008.01.003.
[41] T. Rabczuk, S. Bordas, and G. Zi, “On three-dimensional modelling of crack growth using partition of unity methods,” Comput. Struct., vol. 88, no. 23–24, pp. 1391–1411, 2010, doi: 10.1016/j.compstruc.2008.08.010.
[42] Hughes, T. J. R., Cottrell, J. A., and Bazilevs, Y., “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.
[43] V. P. Nguyen, C. Anitescu, S. P. A. Bordas, and T. Rabczuk, “Isogeometric analysis: An overview and computer implementation aspects,” Math. Comput. Simul., vol. 117, pp. 89–116, 2015, doi: 10.1016/j.matcom.2015.05.008.
[44] S. S. Ghorashi, N. Valizadeh, S. Mohammadi, and T. Rabczuk, “T-spline based XIGA for fracture analysis of orthotropic media,” Comput. Struct., vol. 147, pp. 138–146, 2015, doi: 10.1016/j.compstruc.2014.09.017.
[45] N. Nguyen-Thanh et al., “An extended isogeometric thin shell analysis based on Kirchhoff-Love theory,” Comput. Methods Appl. Mech. Eng., vol. 284, pp. 265–291, 2015, doi: 10.1016/j.cma.2014.08.025.
[46] N. Nguyen-Thanh, H. Nguyen-Xuan, S. P. A. Bordas, and T. Rabczuk, “Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids,” Comput. Methods Appl. Mech. Eng., vol. 200, no. 21–22, pp. 1892–1908, 2011, doi: 10.1016/j.cma.2011.01.018.
[47] N. Nguyen-Thanh et al., “Rotation free isogeometric thin shell analysis using PHT-splines,” Comput. Methods Appl. Mech. Eng., vol. 200, no. 47–48, pp. 3410–3424, 2011, doi: 10.1016/j.cma.2011.08.014.
[48] H. Ghasemi, H. S. Park, and T. Rabczuk, “A level-set based IGA formulation for topology optimization of flexoelectric materials,” Comput. Methods Appl. Mech. Eng., vol. 313, pp. 239–258, 2017, doi: 10.1016/j.cma.2016.09.029.
[49] L. M. Mauludin and C. Oucif, “Modeling of self-healing concrete: A review,” J. Appl. Comput. Mech., vol. 5, no. Special Issue 3, pp. 526–539, 2019, doi: 10.22055/jacm.2017.23665.1167.
[50] C. Oucif and L. M. Mauludin, “Continuum damage-healing and super healing mechanics in brittle materials: A state-of-the-art reviews,” Appl. Sci., vol. 8, no. 12, 2018, doi: 10.3390/app8122350.
[51] L. M. Mauludin, X. Zhuang, and T. Rabczuk, “Computational modeling of fracture in encapsulation-based self-healing concrete using cohesive elements,” Compos. Struct., vol. 196, pp. 63–75, 2018, doi: 10.1016/j.compstruct.2018.04.066.
[52] L. M. Mauludin and C. Oucif, “The effects of interfacial strength on fractured microcapsule,” Front. Struct. Civ. Eng., vol. 13, no. 2, pp. 353–363, 2019, doi: 10.1007/s11709-018-0469-3.
[53] L. M. Mauludin and C. Oucif, “Interaction between matrix crack and circular capsule under uniaxial tension in encapsulation-based self-healing concrete,” Undergr. Sp., vol. 3, no. 3, pp. 181–189, 2018, doi: 10.1016/j.undsp.2018.04.004.
[54] T. B. T. Belytschko, “Elastic crack growth in finite elements with minimal remeshing,” Int. J. Numer. Methods Eng., vol. 45, pp. 601–620, 1990.
[55] Dassault Systèmes Simulia, Analysis User’s Manual, vol. IV. 2012.
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