A novel modification of decouple scaled boundary finite element method in fracture mechanics problems

[1] M. L. Williams, “On the stress distribution at the base of a stationary crack”, Journal of Applied Mechanics,Vol. 24, No. 1, pp. 109-114, (1957).

[2] D. Broek, Elementary engineering fracture mechanics, Springer, (1986).

[3] S. Aoki, K. Kishimoto, H. Kondo, M. Sakata, “Elastodynamic analysis of crack by finite element method using singular element”, International Journal of Fracture,Vol. 14, No. 1, pp. 59-68, (1978).

[4] M. R. Ayatollahi, M. Nejati, “An over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis”, Fatigue and Fracture of Engineering Materials and Structures,Vol. 34, No. 3, pp. 159-176, (2011).

[5] M. Bäker, “Finite element crack propagation calculation using trial cracks”, Computational Materials Science,Vol. 43, No. 1, pp. 179-183, (2008).

[6] E. P. Chen, “Finite element analysis of a bimaterial interface crack”, Theoretical and Applied Fracture Mechanics,Vol. 3, No. 3, pp. 257-262, (1985).

[7] H. G. Delorenzi, “Energy release rate calculations by the finite element method”, Engineering Fracture Mechanics,Vol. 21, No. 1, pp. 129-143, (1985).

[8] R. D. Henshell, K.G. Shaw, “Crack tip finite elements are unnecessary”, International Journal for Numerical Methods in Engineering,Vol. 9, No. 3, pp. 495-507, (1975).

[9] S. Mohammadi, Extended finite element method: for fracture analysis of structures, John Wiley & Sons, (2008).

[10] K. Sharma, T.Q. Bui, C. Zhang, R.R. Bhargava, “Analysis of a subinterface crack in piezoelectric bimaterials with the extended finite element method”, Engineering Fracture Mechanics,Vol. 104, pp. 114-139, (2013).

[11] H. Pathak, A. Singh, I.V. Singh, S.K. Yadav, “Fatigue crack growth simulations of 3-D linear elastic cracks under thermal load by XFEM”, Frontiers of Structural and Civil Engineering,Vol. 9, No. 4, pp. 359-382, (2015).

[12] Q. Z. Xiao, B. L. Karihaloo, “Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery”, International Journal for Numerical Methods in Engineering,Vol. 66, No. 9, pp. 1378-1410, (2006).

[13] A. Portela, M. H. Aliabadi, D. P. Rooke, “Efficient boundary element analysis of sharp notched plates”, International Journal for Numerical Methods in Engineering,Vol. 32, No. 3, pp. 445-470, (1991).

[14] A. Portela, M. H. Aliabadi, D. P. Rooke, “Dual boundary element incremental analysis of crack propagation”, Computers & Structures,Vol. 46, No. 2, pp. 237-247, (1993).

[15] A. L. Saleh, M. H. Aliabadi, “Crack growth analysis in concrete using boundary element method”, Engineering Fracture Mechanics,Vol. 51, No. 4, pp. 533-545, (1995).

[16] A. Ghorbanpoor, J. Zhang, “Boundary element analysis of crack growth for mixed-mode center slant crack problems”, Engineering Fracture Mechanics,Vol. 36, No. 5, pp. 661-668, (1995).

[17] E. D. Leonel, W. S. Venturini, A. Chateauneuf, “A BEM model applied to failure analysis of multi-fractured structures”, Engineering Failure Analysis,Vol. 18, No. 6, pp. 1538-1549, (2011).

[18] M. Treifi, S. O. Oyadiji, “Strain energy approach to compute stress intensity factors for isotropic homogeneous and bi-material V-notches”, International Journal of Solids and Structures, Vol. 50, No. 14-15,pp. 2196-2212, (2013).

[19] G. Meneghetti, B. Atzori, A. Campagnolo, F. Berto, “A link between the peak stresses and the averaged strain energy density for cracks under mixed-mode (I+II) loading”, Frattura ed Integrita Strutturale,Vol. 9, No. 34, pp. 109-115, (2015) .

[20] N. O. Larrosa, M. Treifi, R.A. Ainsworth, “Rapid parametric analysis of SEN(T) specimens using algorithmic modelling: Evaluation of strain energy density and notch stress intensity factors”, Materials and Design, Vol. 85, pp. 771-777, (2015).

[21] P. Liu, T. Yu, T.Q. Bui, C. Zhang, “Transient dynamic crack analysis in non-homogeneous functionally graded piezoelectric materials by the X-FEM”, Computational Materials Science,Vol. 69,pp. 542-558, (2013).

[22] D. Racz, T.Q. Bui, “Novel adaptive meshfree integration techniques in meshlessmethods”, International Journal for Numerical Methods in Engineering,Vol. 90, No. 11, pp. 1414-1434, (2012).

[23] B. N. Rao, S. Rahman, “Probabilistic fracture mechanics by Galerkin meshless methods - Part I: Rates of stress intensity factors”, Computational Mechanics,Vol. 28, 351-364, (2002).

[24] N. T. Nguyen, T.Q. Bui, C. Zhang, T.T. Truong, “Crack growth modeling in elastic solids by the extended meshfree Galerkin radial point interpolation method”, Engineering Analysis with Boundary Elements,Vol. 44, pp. 87-97, (2014).

[25] S. Rajagopal, N. Gupta, “Meshfree modelling of fracture-a comparative study of different methods, Meccanica”, Vol. 46, No. 5, pp. 1145-1158, (2011).

[26] A. Asadpour, “Thermo-elastic extended meshfree method for fracture without crack tip enrichment”, Frontiers of Structural and Civil Engineering, Vol. 9, No. 6, pp. 441-447, (2015).

[27] A. Y. T. Leung, R. K. L. Su, “Mode I crack problems by fractal two level finite element methods”, Engineering Fracture Mechanics,Vol. 48, 847-856, (1994).

[28] J. Y. Liu, F. L. Xu, B. K. Ning, H. Fan, “Evaluation of the T-stress and the higher order terms of the elastic crack based on the SBFEM”, Advanced Materials Research,Vol. 838, pp. 2275-2278, (2014).

[29] C. Song, J. P. “Wolf, Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method”, Computers and Structures,Vol. 80, No. 2, pp. 183-197, (2002).

[30] S. R. Chidgzey, A. J. Deeks, “Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method”, Engineering Fracture Mechanics,Vol. 72, No. 13, pp. 2019-2036, (2005).

[31] Z. J. Yang, E. T. Ooi, “Recent progress in modeling crack propagation using the scaled boundary finite element method”, International Journal of Computational Methods,Vol. 9, No. 1, pp. 1-24, (2012).

[32] M. G. Shi, C. M. Song, H. Zhong, Y. J. Xu, C. H. Zhang, “A coupled SBFEM-FEM approach for evaluating stress intensity factors”,Applied Mechanics and Materials, Vol. 353, pp. 3369-3377, (2013).

[33] G. E. Bird, J. Trevelyan, C. E. Augarde, “A coupled BEM/scaled boundary FEM formulation for accurate computations in linear elastic fracture mechanics”, Engineering Analysis with Boundary Elements,Vol. 34, No. 6, pp. 599-610, (2010).

[34] B. N. Rao, S. Rahman, “A coupled meshless-finite element method for fracture analysis of cracks”, International Journal of Pressure Vessels and Piping,Vol. 78, No. 9, pp. 647-657, (2001).

[35] S. R. Chidgzey, J. Trevelyan, A. J. Deeks, “Coupling of the boundary element method and the scaled boundary finite element method for computations in fracture mechanics”, Computers and Structures,Vol. 86, No. 11-12, 1198-1203, (2008).

[36] Y. T. Gu, L. C. Zhang, “Coupling of the meshfree and finite element methods for determination of the crack tip fields”, Engineering Fracture Mechanics,Vol. 75, No. 5, pp. 986-1004, (2008).

[37] N. Khaji, M.I. Khodakarami, “A new semi-analytical method with diagonal coefficient matrices for potential problems”, Engineering Analysis with Boundary Elements,Vol. 35, No. 6, 845-854, (2011).

[38] M. I. Khodakarami, N. Khaji, “Analysis of elastostatic problems using a semi-analytical method with diagonal coefficient matrices”, Engineering Analysis with Boundary Elements,Vol. 35, No. 12, pp. 1288-1296, (2011).

[39] M. I. Khodakarami, N. Khaji, M. T. Ahmadi, “Modeling transient elastodynamic problems using a novel semi-analytical method yielding decoupled partial differential equations”, Computer Methods in Applied Mechanics and Engineering,Vol. 213–216, No. 0, pp. 183-195, (2012).

[40] N. Khaji, M. Yazdani, “Determination of stress intensity factors of 2D fracture mechanics problems through a new semi-analytical method”, Fatigue & Fracture of Engineering Materials & Structures,Vol. 39, No. 4, pp. 467-478, (2016).

[41] M. Yazdani, N. Khaji, M. Khodakarami, “Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate”, Acta Mechanica,Vol. 227, No. 12,pp. 3529-3547, (2016).

[42] M. Yazdani, N. Khaji, M. Khodakarami, “Development of a new semi-analytical approach for 2D analysis of crack propagation     problems”,     Fatigue    & Fracture of Engineering Materials & Structures,1-20, (2018).

[43] M. I. Khodakarami, M. Fakharian, “A new   modification   in  decoupled  scaled boundary method with diagonal coefficient matrices for analysis of 2D elastostatic and transient elastodynamic problems”, Asian Journal of Civil Engineering,Vol. 16, No. 5, pp. 709-732, (2015).

[44] F. Berto, P. Lazzarin, “On higher order terms in the crack tip stress field”, International Journal of Fracture,Vol. 161, No. 2, pp. 221-226, (2010).

[45] J. R. Rice, “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks”, Journal of Applied Mechanics,Vol. 35, No. 2, 379-386, (1968).

[46] D. Nunez, K. S. Surana, A. Romkes, J. N. Reddy, “J-Integral for Mode I Linear Elastic Fracture Mechanics in h, p, k Mathematical and Computational Framework”, International Journal for Computational Methods in Engineering Science and Mechanics,Vol. 10, No. 5, pp. 345-369, (2009).

[47] H. G. deLorenzi, “On the energy release rate and the J-integral for 3-D crack configurations”, International Journal of Fracture,Vol. 19, No. 3, pp. 183-193, (1982).

[48] H. Tada, “Westergaard stress functions for several periodic crack problems”, Engineering Fracture Mechanics,Vol. 2, No. 2, pp. 177-180, (1970).

[49] M. S. Chowdhury, C. Song, W. Gao, “Probabilistic fracture mechanics by using Monte Carlo simulation and the scaled boundary finite element method”, Engineering Fracture Mechanics,Vol. 78, No. 12, pp. 2369-2389, (2011).

[50] T. K. Hellen, W. S. Blackburn, “The calculation of stress intensity factors for combined tensile and shear loading”, International Journal of Fracture,Vol. 11, No. 4, pp. 605-617, (1975).