×

zbMATH — the first resource for mathematics

A quasi-static crack propagation simulation based on shape-free hybrid stress-function finite elements with simple remeshing. (English) Zbl 1296.74134
Summary: A new shape-free multi-node singular hybrid stress-function (HSF) element and a shape-free 8-node plane HSF element proposed recently are employed to simulate the quasi-static 2D crack propagation problem. Compared with other well-known methods, such new scheme exhibits four advantages: (i) for the singular element, the shape and the number of nodes can be flexibly adjusted as required; (ii) high precision for stress intensity factors (SIF) can be obtained due to the advantages of the HSF method; (iii) only simple remeshing with a very coarse mesh is needed for each simulation step; (iv) unstructured mesh containing extremely distorted elements can be used without losing precision. It demonstrates that the proposed scheme is an effective technique for dealing with crack propagation problems.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R99 Fracture and damage
Software:
XFEM; ABAQUS
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Henshell, R. D.; Shaw, K. G., Crack tip finite elements are unnecessary, Int. J. Numer. Methods Eng., 9, 3, 495-507, (1975) · Zbl 0306.73064
[2] Barsoum, R. S., On the use of isoparametric finite elements in linear fracture mechanics, Int. J. Numer. Methods Eng., 10, 1, 25-37, (1976) · Zbl 0321.73067
[3] Barsoum, R. S., Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements, Int. J. Numer. Methods Eng., 11, 1, 85-98, (1977) · Zbl 0348.73030
[4] Lynn, P. P.; Ingraffea, A. R., Transition elements to be used with quarter-point crack-tip elements, Int. J. Numer. Methods Eng., 12, 6, 1031-1036, (1978)
[5] Belytschko, T.; Black, T., Elastic crack growth in finite elements with minimal remeshing, Int. J. Numer. Methods Eng., 45, 601-620, (1999) · Zbl 0943.74061
[6] Moës, N.; Dolbow, J.; Belytschko, T., A finite element method for crack growth without remeshing, Int. J. Numer. Methods Eng., 46, 131-150, (1999) · Zbl 0955.74066
[7] Daux, C.; Moës, N.; Dolbow, J.; Sukumar, N.; Belytschko, T., Arbitrary branched and intersecting cracks with the extended finite element method, Int. J. Numer. Methods Eng., 48, 1741-1760, (2000) · Zbl 0989.74066
[8] Belytschko, T.; Moës, N.; Usui, S.; Parimi, C., Arbitrary discontinuities in finite elements, Int. J. Numer. Methods Eng., 50, 993-1013, (2001) · Zbl 0981.74062
[9] Huang, R.; Sukumar, N.; Prévost, J. H., Modeling quasi-static crack growth with the extended finite element method. part II: numerical applications, Int. J. Solids Struct., 40, 7539-7552, (2003) · Zbl 1064.74163
[10] Richardson, C. L.; Hegemann, J.; Sifakis, E.; Hellrung, J.; Teran, J. M., An XFEM method for modeling geometrically elaborate crack propagation in brittle materials, Int. J. Numer. Methods Eng., 88, 1042-1065, (2011) · Zbl 1242.74156
[11] Li, S.; Ghosh, S., Extended Voronoi cell finite element model for multiple cohesive crack propagation in brittle materials, Int. J. Numer. Methods Eng., 65, 1028-1067, (2006) · Zbl 1179.74152
[12] Bordas, S. P.A.; Rabczuk, T.; Hung, N. X.; Nguyen, V. P.; Natarajan, S.; Bog, T.; Quan, D. M.; Hiep, N. V., Strain smoothing in FEM and XFEM, Comput. Struct., 88, 1419-1443, (2010)
[13] Vu-Bac, N.; Nguyen-Xuan, H.; Chen, L.; Bordas, S.; Kerfriden, P.; Simpson, R. N.; Liu, G. R.; Rabczuk, T., A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis, CMES - Comput. Model. Eng. Sci., 73, 331-356, (2011) · Zbl 1231.74444
[14] Zamani, A.; Eslami, M. R., Embedded interfaces by polytope FEM, Int. J. Numer. Methods Eng., 88, 715-748, (2011) · Zbl 1242.74176
[15] Dujc, J.; Brank, B.; Ibrahimbegovic, A., Stress-hybrid quadrilateral finite element with embedded strong discontinuity for failure analysis of plane stress solids, Int. J. Numer. Methods Eng., 94, 1075-1098, (2013) · Zbl 1352.74346
[16] Ooi, E. T.; Yang, Z. J., A hybrid finite element-scaled boundary finite element method for crack propagation modeling, Comput. Methods Appl. Mech. Eng., 199, 17, 1178-1192, (2010) · Zbl 1227.74084
[17] Ooi, E. T.; Yang, Z. J., Modelling dynamic crack propagation using the scaled boundary finite element method, Int. J. Numer. Methods Eng., 88, 4, 329-349, (2011) · Zbl 1242.74145
[18] Ooi, E. T.; Song, C.; Tin-Loi, F.; Yang, Z. J., Polygon scaled boundary finite elements for crack propagation modelling, Int. J. Numer. Methods Eng., 91, 319-342, (2012) · Zbl 1246.74062
[19] Nourbakhshnia, N.; Liu, G. R., A quasi-static crack growth simulation based on the singular ES-FEM, Int. J. Numer. Methods Eng., 88, 5, 473-492, (2011) · Zbl 1242.74144
[20] Nguyen-Xuan, H.; Liu, G. R.; Nourbakhshnia, N.; Chen, L., A novel singular ES-FEM for crack growth simulation, Eng. Fract. Mech., 84, 41-66, (2012)
[21] Nguyen-Xuan, H.; Liu, G. R.; Bordas, S.; Natarajan, S.; Rabczuk, T., An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order, Comput. Methods Appl. Mech. Eng., 253, 252-273, (2013) · Zbl 1297.74126
[22] Tong, P.; Pian, T. H.H.; Lasry, S. J., A hybrid-element approach to crack problems, Int. J. Numer. Methods Eng., 7, 297-308, (1973) · Zbl 0264.73113
[23] Teixeira De Freitas, J. A.; Ji, Z. Y., Hybrid-Trefftz equilibrium model for crack problems, Int. J. Numer. Methods Eng., 39, 569-584, (1996) · Zbl 0845.73073
[24] Long, Y. Q.; Cen, S.; Long, Z. F., Advanced finite element method in structural engineering, (2009), Springer-Verlag GmbH, Tsinghua University Press Berlin, Heidelberg, Beijing · Zbl 1168.74005
[25] Long, Y. Q.; Zhao, Y. Q., Calculation of stress intensity factors in plane problems by the sub-region mixed finite element method, Eng. Software, 7, 1, 32-35, (1985)
[26] Huang, M. F.; Long, Y. Q., Calculation of stress intensity factors of cracked Reissner plates by the sub-region mixed finite element method, Comput. Struct., 30, 4, 837-840, (1988) · Zbl 0671.73080
[27] Long, Y. Q.; Qian, J., Calculation of stress intensity factors for surface cracks in a 3D body by the subregion mixed FEM, Comput. Struct., 44, 1/2, 75-78, (1992) · Zbl 0825.73738
[28] Fan, Z.; Long, Y. Q., Sub-region mixed finite element analysis of V-notched plates, Int. J. Fract., 56, 333-344, (1992)
[29] Cen, S.; Fu, X. R.; Zhou, M. J., 8- and 12-node plane hybrid stress-function elements immune to severely distorted mesh containing elements with concave shapes, Comput. Methods Appl. Mech. Eng., 200, 29-32, 2321-2336, (2011) · Zbl 1230.74173
[30] Fu, X. R.; Cen, S.; Li, C. F.; Chen, X. M., Analytical trial function method for development of new 8-node plane element based on the variational principle containing Airy stress function, Eng. Comput., 27, 4, 442-463, (2010) · Zbl 1257.74149
[31] Cen, S.; Zhou, M. J.; Fu, X. R., A 4-node hybrid stress-function (HS-F) plane element with drilling degrees of freedom less sensitive to severe mesh distortions, Comput. Struct., 89, 5-6, 517-528, (2011)
[32] Cen, S.; Fu, X. R.; Zhou, G. H.; Zhou, M. J.; Li, C. F., Shape-free finite element method: the plane hybrid stress-function (HS-F) element method for anisotropic materials, Sci. China Phys. Mech. Astron., 54, 4, 653-665, (2011)
[33] Cen, S.; Zhou, M. J.; Shang, Y., Shape-free finite element method: another way between mesh and mesh-free methods, Math. Prob. Eng., 2013, 491626, (2013) · Zbl 1296.74106
[34] Pian, T. H.H., Derivation of element stiffness matrices by assumed stress distributions, AIAA J., 2, 7, 1333-1336, (1964)
[35] Williams, M. L., On the stress distribution at the base of a stationary crack, J. Appl. Mech., 24, 109-114, (1957) · Zbl 0077.37902
[36] Yau, J.; Wang, S.; Corten, H., A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity, J. Appl. Mech., 47, 335-341, (1980) · Zbl 0463.73103
[37] Tanaka, S.; Okada, H.; Okazawa, S.; Fujikubo, M., Fracture mechanics analysis using the wavelet Galerkin method and extended finite element method, Int. J. Numer. Methods Eng., 93, 1082-1108, (2013) · Zbl 1352.74027
[38] Dassault Systémes Simulia Corp., Abaqus Theory Manual, Version 6.12, Dassault Systémes Simulia Corp., Providence, RI, USA 2012.
[39] Bittencourt, T. N.; Wawrzynek, P. A.; Ingraffea, A. R.; Sousa, J. L., Quasi-automatic simulation of crack propagation for 2D LEFM problems, Eng. Fract. Mech., 55, 321-334, (1996)
[40] Geniaut, S.; Galenne, E., Simple method for crack growth in mixed mode with X-FEM, Int. J. Solids Struct., 49, 2094-2106, (2012)
[41] Häusler, S. M.; Lindhorst, K.; Horst, P., Combination of the material force concept and the extended finite element method for mixed mode crack growth simulations, Int. J. Numer. Methods Eng., 85, 1522-1542, (2011) · Zbl 1217.74122
[42] Passieux, J. C.; Réthoré, J. L.; Gravouil, A.; Baietto, Marie-Christine, Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver, Comput. Mech., 52, 1381-1393, (2013) · Zbl 06272148
[43] Hughes, T. J.R.; Cottrell, J. A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Eng., 194, 4135-4195, (2005) · Zbl 1151.74419
[44] Bazilevs, Y.; Calo, V. M.; Cottrell, J. A.; Evans, J. A.; Hughes, T. J.R.; Lipton, S.; Scott, M. A.; Sederberg, T. W., Isogeometric analysis using T-splines, Comput. Methods Appl. Mech. Eng., 199, 5-8, 229-263, (2010) · Zbl 1227.74123
[45] Nguyen-Thanh, N.; Kiendl, J.; Nguyen-Xuan, H.; Wüchner, R.; Bletzinger, K. U.; Bazilevs, Y.; Rabczuk, T., Rotation free isogeometric thin shell analysis using PHT-splines, Comput. Methods Appl. Mech. Eng., 200, 47-48, 3410-3424, (2011) · Zbl 1230.74230
[46] Nguyen, V. P.; Nguyen-Xuan, H., High-order B-splines based finite elements for the delamination analysis of laminated composites, Compos. Struct., 102, 261-275, (2013)
[47] Thai, C. H.; Ferreira, A. J.M.; Carrera, E.; Nguyen-Xuan, H., Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory, Compos. Struct., 104, 196-214, (2013)
[48] Nguyen-Xuan, H.; Thai, C. H.; Nguyen-Thoi, T., Isogeometric finite element analysis of composite sandwich plates using a new higher order shear deformation theory, Compos. Part B, 55, 558-574, (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.