A singular edge-based smoothed finite element method (ES-FEM) for bimaterial interface cracks.

*(English)*Zbl 1398.74316Summary: The recently developed edge-based smoothed finite element method (ES-FEM) is extended to the mix-mode interface cracks between two dissimilar isotropic materials. The present ES-FEM method uses triangular elements that can be generated automatically for problems even with complicated geometry, and strains are smoothed over the smoothing domains associated with the edges of elements. Considering the stress singularity in the vicinity of the bimaterial interface crack tip is of the inverse square root type together with oscillatory nature, a five-node singular crack tip element is devised within the framework of ES-FEM to construct singular shape functions. Such a singular element can be easily implemented since the derivatives of the singular shape term \({(1/\sqrt r)}\) are not needed. The mix-mode stress intensity factors can also be easily evaluated by an appropriate treatment during the domain form of the interaction integral. The effectiveness of the present singular ES-FEM is demonstrated
via benchmark examples for a wide range of material combinations and boundary conditions.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74R05 | Brittle damage |

74R10 | Brittle fracture |

74B05 | Classical linear elasticity |

##### Keywords:

interface crack; numerical method; meshfree method; stress intensity factor; \(J\)-integral; energy release rate; ES-FEM; singularity
PDF
BibTeX
XML
Cite

\textit{L. Chen} et al., Comput. Mech. 45, No. 2--3, 109--125 (2010; Zbl 1398.74316)

Full Text:
DOI

##### References:

[1] | Yeap KB, Zeng KY, Chi DZ (2008) Determining the interfacial toughness of low-k films on Si substrate by wedge indentation: further studies. Acta Mater 56: 977–984 |

[2] | Hutchinson JW, Suo Z (1992) Mixed mode cracking in layered materials. In: Hutchinson JW, Wu TY (eds) Advances in applied mechanics, pp 63–191 · Zbl 0790.73056 |

[3] | Williams ML (1959) The stress around a fault or crack in dissimilar media. Bullet Seismol Soc Am 49: 199–204 |

[4] | England AH (1965) A crack between dissimilar media. J Appl Mech 32: 400–402 |

[5] | Rice JR, Sih GC (1965) Plane problems of cracks in dissimilar media. J Appl Mech 32: 418–423 |

[6] | Rice JR (1988) Elastic fracture mechanics concepts for interfacial cracks. J Appl Mech 55: 98–103 |

[7] | Henshell RD, Shaw KG (1975) Crack tip finite elements are unnecessary. Int J Numer Methods Eng 9: 495–507 · Zbl 0306.73064 |

[8] | Barsoum RS (1976) On the use of isoparametric finite elements in linear fracture mechanics. Int J Numer Methods Eng 10: 551–564 · Zbl 0325.73092 |

[9] | Barsoum RS (1977) Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements. Int J Numer Methods Eng 11: 85–98 · Zbl 0348.73030 |

[10] | Shih CF, Asaro RJ (1988) Elastic-plastic analysis of cracks on bimaterial interfaces: part I-small scale yielding. J Appl Mech 55: 299–316 |

[11] | Matos PPL, McMeeking RM, Charalambides PG, Drory MD (1989) A method for calculating stress intensities in bimaterial fracture. Int J Fract 40: 235–254 |

[12] | Nahta R, Moran B (1993) Domain integrals for axisymmetric interface crack problems. Int J Solids Struct 30(15): 2027–2040 · Zbl 0782.73060 |

[13] | Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5): 601–620 · Zbl 0943.74061 |

[14] | Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1): 131–150 · Zbl 0955.74066 |

[15] | Belytschko T, Moes N, Usui S, Parimi C (2001) Arbitrary discontinuities in finite elements. Int J Numer Methods Eng 50(4): 993–1013 · Zbl 0981.74062 |

[16] | Sukumar N, Huang ZY, PrĂ©vost JH, Suo Z (2004) Partition of unity enrichment for bimaterial interface cracks. Int J Numer Methods Eng 59: 1075–1102 · Zbl 1041.74548 |

[17] | Chen JS, Wu CT, Yoon Y (2001) A stabilized conforming nodal integration for Galerkin mesh-free methods. Int J Numer Methods Eng 50: 435–466 · Zbl 1011.74081 |

[18] | Liu GR, Dai KY, Nguyen TT (2007) A smoothed finite element method for mechanics problems. Comput Mech 39: 859–877 · Zbl 1169.74047 |

[19] | Liu GR, Nguyen TT, Dai KY, Lam KY (2007) Theoretical aspects of the smoothed finite element method (SFEM). Int J Numer Methods Eng 71: 902–930 · Zbl 1194.74432 |

[20] | Liu GR, Nguyen-Thoi T, Lam KY (2008) A node-based smoothed finite element method for upper bound solution to solid problems (NS-FEM). Comput Struct 87: 14–26 |

[21] | Dohrmann CR, Heinstein MW, Jung J, Key SW, Witkowski WR (2000) Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes. Int J Numer Methods Eng 47: 1549–1568 · Zbl 0989.74067 |

[22] | Liu GR, Zhang GY, Dai KY, Wang YY, Zhong ZH, Li GY, Han X (2005) A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems. Int J Comput Methods 2(4): 645–665 · Zbl 1137.74303 |

[23] | Liu GR, Nguyen-Thoi T, Lam KY (2009) An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analysis. J Sound Vib 320: 1100–1130 |

[24] | Nguyen-Thoi T, Liu GR, Lam KY (2009) A face-based smoothed finite element method (FS-FEM) for 3D linear and nonlinear solid mechanics problems using 4-node tetrahedral elements. Int J Numer Methods Eng 78: 324–353 · Zbl 1183.74299 |

[25] | Liu GR, Gu YT (2001) A point interpolation method for two-dimensional solids. Int J Numer Methods Eng 50: 937–951 · Zbl 1050.74057 |

[26] | Liu GR, Zhang GY (2008) Edge-based smoothed point interpolation methods. Int J Comput Methods 5: 621–646 · Zbl 1264.74284 |

[27] | Chen L, Nguyen-Xuan H, Nguyen-Thoi T, Zeng KY, Wu SC (2009) Assessment of smoothed point interpolation methods for elastic mechanics. Commu Numer Methods Eng doi: 10.1002/cnm.1251 · Zbl 1323.74080 |

[28] | Shih CF (1988) Cracks on bimaterial interfaces: elasticity and plasticity aspects. Mater Sci Eng A 143: 77–90 |

[29] | Dundurs J (1969) Edge-bonded dissimilar orthogonal elastic wedges. J Appl Mech 36: 650–652 |

[30] | Moran B, Shih CF (1987) Crack tip and associated domain integrals from momentum and energy balance. Eng Fract Mech 27(6): 615–641 |

[31] | Li FZ, Shih CF, Needleman A (1985) A comparison of methods for calculating energy release rates. Eng Fract Mech 21(2): 405–421 |

[32] | Charalambides PG, Lund J, Evans AG, McMeeking RM (1989) A test specimen for determining the fracture resistance of bimaterial interfaces. J Appl Mech 56: 77–82 |

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.