How to cite this paper
Alshoaibi, A. (2020). Finite element-based model for crack propagation in linear elastic materials.Engineering Solid Mechanics, 8(2), 131-142.
Refrences
Abd-Elhady, A. (2013). Mixed mode I/II stress intensity factors through the thickness of disc type specimens. Engineering Solid Mechanics, 1(4), 119-128.
Akbardoost, J., Ayatollahi, M. R., Aliha, M. R. M., Pavier, M. J., & Smith, D. J. (2014). Size-dependent fracture behavior of Guiting limestone under mixed mode loading. International Journal of Rock Mechanics and Mining Sciences, 71, 369-380.
Aliha, M. R. M., & Ayatollahi, M. R. (2008). On mixed-mode I/II crack growth in dental resin materials. Scripta Materialia, 59(2), 258-261.
Aliha, M. R. M., & Ayatollahi, M. R. (2012). Analysis of fracture initiation angle in some cracked ceramics using the generalized maximum tangential stress criterion. International Journal of Solids and Structures, 49(13), 1877-1883.
Aliha, M. R. M., & Rezaei, M. (2011). Experimental and theoretical study of fracture paths in brittle cracked materials subjected to pure mode II loading. In Applied Mechanics and Materials (Vol. 70, pp. 159-164). Trans Tech Publications.
Aliha, M. R. M., & Saghafi, H. (2013). The effects of thickness and Poisson’s ratio on 3D mixed-mode fracture. Engineering Fracture Mechanics, 98, 15-28.
Aliha, M. R. M., Ayatollahi, M. R., Smith, D. J., & Pavier, M. J. (2010). Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Engineering Fracture Mechanics, 77(11), 2200-2212.
Aliha, M. R. M., Bahmani, A., & Akhondi, S. (2016a). Mixed mode fracture toughness testing of PMMA with different three-point bend type specimens. European Journal of Mechanics-A/Solids, 58, 148-162.
Aliha, M. R. M., Berto, F., Bahmani, A., & Gallo, P. (2017). Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion. Physical Mesomechanics, 20(2), 149-156.
Aliha, M. R. M., Berto, F., Bahmani, A., Akhondi, S., & Barnoush, A. (2016b). Fracture assessment of polymethyl methacrylate using sharp notched disc bend specimens under mixed mode I+ III loading. Physical Mesomechanics, 19(4), 355-364.
Alshoaibi, A. M., & Ariffin, A. K. (2006). Finite element simulation of stress intensity factors in elastic-plastic crack growth. Journal of Zhejiang University-SCIENCE A, 7(8), 1336-1342.
Atluri, S. N. (1982). Path-independent integrals in finite elasticity and inelasticity, with body forces, inertia, and arbitrary crack-face conditions. Engineering Fracture Mechanics, 16(3), 341-364.
Ayatollahi, M. R., & Aliha, M. R. M. (2007). Wide range data for crack tip parameters in two disc-type specimens under mixed mode loading. Computational materials science, 38(4), 660-670.
Ayatollahi, M. R., & Aliha, M. R. M. (2009). Analysis of a new specimen for mixed mode fracture tests on brittle materials. Engineering Fracture Mechanics, 76(11), 1563-1573.
Ayatollahi, M. R., Aliha, M. R. M., & Hassani, M. M. (2006). Mixed mode brittle fracture in PMMA—an experimental study using SCB specimens. Materials Science and Engineering: A, 417(1-2), 348-356.
Ayatollahi, M. R., Aliha, M. R. M., & Saghafi, H. (2011). An improved semi-circular bend specimen for investigating mixed mode brittle fracture. Engineering Fracture Mechanics, 78(1), 110-123.
Azócar, D., Elgueta, M., & Rivara, M. C. (2010). Automatic LEFM crack propagation method based on local Lepp–Delaunay mesh refinement. Advances in Engineering Software, 41(2), 111-119.
Belytschko, T., & Black, T. (1999). Elastic crack growth in finite elements with minimal remeshing. International journal for numerical methods in engineering, 45(5), 601-620.
Belytschko, T., Lu, Y. Y., & Gu, L. (1994). Element‐free Galerkin methods. International journal for numerical methods in engineering, 37(2), 229-256.
Benvenuti, E. (2017). An effective XFEM with equivalent eigenstrain for stress intensity factors of homogeneous plates. Computer Methods in Applied Mechanics and Engineering, 321, 427-454.
Boulenouar, A., Benseddiq, N., Mazari, M., & Benamara, N. (2014). FE model for linear-elastic mixed mode loading: estimation of SIFs and crack propagation. Journal of Theoretical and Applied Mechanics, 52.
Cooke, M. L., & Pollard, D. D. (1996). Fracture propagation paths under mixed mode loading within rectangular blocks of polymethyl methacrylate. Journal of Geophysical Research: Solid Earth, 101(B2), 3387-3400.
Dehghany, M., Saeidi Googarchin, H., & Aliha, M. R. M. (2017). The role of first non‐singular stress terms in mixed mode brittle fracture of V‐notched components: an experimental study. Fatigue & Fracture of Engineering Materials & Structures, 40(4), 623-641.
Duarte, C. A., & Oden, J. T. (1996). H‐p clouds—an h‐p meshless method. Numerical Methods for Partial Differential Equations: An International Journal, 12(6), 673-705.
Guo, L., Xiang, J., Latham, J. P., & Izzuddin, B. (2016). A numerical investigation of mesh sensitivity for a new three-dimensional fracture model within the combined finite-discrete element method. Engineering Fracture Mechanics, 151, 70-91.
Khan, S. M., & Khraisheh, M. K. (2000). Analysis of mixed mode crack initiation angles under various loading conditions. Engineering Fracture Mechanics, 67(5), 397-419.
Khan, S. M., & Khraisheh, M. K. (2004). A new criterion for mixed mode fracture initiation based on the crack tip plastic core region. International Journal of Plasticity, 20(1), 55-84.
Lan, M., Waisman, H., & Harari, I. (2013). A High‐order extended finite element method for extraction of mixed‐mode strain energy release rates in arbitrary crack settings based on Irwin's integral. International Journal for Numerical Methods in Engineering, 96(12), 787-812.
Liu, Y. J., Li, Y. X., & Xie, W. (2017). Modeling of multiple crack propagation in 2-D elastic solids by the fast multipole boundary element method. Engineering Fracture Mechanics, 172, 1-16.
Matvienko, Y. G. (2012). Maximum average tangential stress criterion for prediction of the crack path. International Journal of Fracture, 176(1), 113-118.
Miller, E. E., Sutton, M. A., Deng, X., Watts, H., Reynolds, A. P., Ke, X., & Schreier, H. W. (2015). Experimental and predicted crack paths for Al-2024-T351 under mixed-mode I/II fatigue. In Fracture, Fatigue, Failure, and Damage Evolution, Volume 5 (pp. 11-20). Springer, Cham.
Mirsayar, M. M., Aliha, M. R. M., & Samaei, A. T. (2014). On fracture initiation angle near bi-material notches–Effects of first non-singular stress term. Engineering fracture mechanics, 119, 124-131.
Mirsayar, M. M., Razmi, A., Aliha, M. R. M., & Berto, F. (2018). EMTSN criterion for evaluating mixed mode I/II crack propagation in rock materials. Engineering Fracture Mechanics, 190, 186-197.
Rao, B. N., & Rahman, S. (2001). A coupled meshless-finite element method for fracture analysis of cracks. International Journal of Pressure Vessels and Piping, 78(9), 647-657.
Razavi, S. M. J., Aliha, M. R. M., & Berto, F. (2018). Application of an average strain energy density criterion to obtain the mixed mode fracture load of granite rock tested with the cracked asymmetric four-point bend specimens. Theoretical and Applied Fracture Mechanics, 97, 419-425.
Rice, J. R. (1968). A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of applied mechanics, 35(2), 379-386.
Sabbagh-Yazdi, S. R., Farhoud, A., & Gharebaghi, S. A. (2018). Simulation of 2D linear crack growth under constant load using GFVM and two-point displacement extrapolation method. Applied Mathematical Modelling, 61, 650-667.
Sutton, M. A., Boone, M. L., Ma, F., & Helm, J. D. (2000). A combined modeling–experimental study of the crack opening displacement fracture criterion for characterization of stable crack growth under mixed mode I/II loading in thin sheet materials. Engineering Fracture Mechanics, 66(2), 171-185.
Tada, H., Paris, P., & Irwin, G. (2000). The analysis of cracks handbook. New York: ASME Press, 2, 1.
Varfolomeev, I., Burdack, M., Moroz, S., Siegele, D., & Kadau, K. (2014). Fatigue crack growth rates and paths in two planar specimens under mixed mode loading. International Journal of Fatigue, 58, 12-19.
Williams, M. L. (1957). The bending stress distribution at the base of a stationary crack. Trans. ASME, 79, 109-114.
Xie, D., & Waas, A. M. (2006). Discrete cohesive zone model for mixed-mode fracture using finite element analysis. Engineering fracture mechanics, 73(13), 1783-1796.
Zhang, R., & Guo, R. (2018). Determination of crack tip stress intensity factors by singular Voronoi cell finite element model. Engineering Fracture Mechanics, 197, 206-216.
Akbardoost, J., Ayatollahi, M. R., Aliha, M. R. M., Pavier, M. J., & Smith, D. J. (2014). Size-dependent fracture behavior of Guiting limestone under mixed mode loading. International Journal of Rock Mechanics and Mining Sciences, 71, 369-380.
Aliha, M. R. M., & Ayatollahi, M. R. (2008). On mixed-mode I/II crack growth in dental resin materials. Scripta Materialia, 59(2), 258-261.
Aliha, M. R. M., & Ayatollahi, M. R. (2012). Analysis of fracture initiation angle in some cracked ceramics using the generalized maximum tangential stress criterion. International Journal of Solids and Structures, 49(13), 1877-1883.
Aliha, M. R. M., & Rezaei, M. (2011). Experimental and theoretical study of fracture paths in brittle cracked materials subjected to pure mode II loading. In Applied Mechanics and Materials (Vol. 70, pp. 159-164). Trans Tech Publications.
Aliha, M. R. M., & Saghafi, H. (2013). The effects of thickness and Poisson’s ratio on 3D mixed-mode fracture. Engineering Fracture Mechanics, 98, 15-28.
Aliha, M. R. M., Ayatollahi, M. R., Smith, D. J., & Pavier, M. J. (2010). Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Engineering Fracture Mechanics, 77(11), 2200-2212.
Aliha, M. R. M., Bahmani, A., & Akhondi, S. (2016a). Mixed mode fracture toughness testing of PMMA with different three-point bend type specimens. European Journal of Mechanics-A/Solids, 58, 148-162.
Aliha, M. R. M., Berto, F., Bahmani, A., & Gallo, P. (2017). Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion. Physical Mesomechanics, 20(2), 149-156.
Aliha, M. R. M., Berto, F., Bahmani, A., Akhondi, S., & Barnoush, A. (2016b). Fracture assessment of polymethyl methacrylate using sharp notched disc bend specimens under mixed mode I+ III loading. Physical Mesomechanics, 19(4), 355-364.
Alshoaibi, A. M., & Ariffin, A. K. (2006). Finite element simulation of stress intensity factors in elastic-plastic crack growth. Journal of Zhejiang University-SCIENCE A, 7(8), 1336-1342.
Atluri, S. N. (1982). Path-independent integrals in finite elasticity and inelasticity, with body forces, inertia, and arbitrary crack-face conditions. Engineering Fracture Mechanics, 16(3), 341-364.
Ayatollahi, M. R., & Aliha, M. R. M. (2007). Wide range data for crack tip parameters in two disc-type specimens under mixed mode loading. Computational materials science, 38(4), 660-670.
Ayatollahi, M. R., & Aliha, M. R. M. (2009). Analysis of a new specimen for mixed mode fracture tests on brittle materials. Engineering Fracture Mechanics, 76(11), 1563-1573.
Ayatollahi, M. R., Aliha, M. R. M., & Hassani, M. M. (2006). Mixed mode brittle fracture in PMMA—an experimental study using SCB specimens. Materials Science and Engineering: A, 417(1-2), 348-356.
Ayatollahi, M. R., Aliha, M. R. M., & Saghafi, H. (2011). An improved semi-circular bend specimen for investigating mixed mode brittle fracture. Engineering Fracture Mechanics, 78(1), 110-123.
Azócar, D., Elgueta, M., & Rivara, M. C. (2010). Automatic LEFM crack propagation method based on local Lepp–Delaunay mesh refinement. Advances in Engineering Software, 41(2), 111-119.
Belytschko, T., & Black, T. (1999). Elastic crack growth in finite elements with minimal remeshing. International journal for numerical methods in engineering, 45(5), 601-620.
Belytschko, T., Lu, Y. Y., & Gu, L. (1994). Element‐free Galerkin methods. International journal for numerical methods in engineering, 37(2), 229-256.
Benvenuti, E. (2017). An effective XFEM with equivalent eigenstrain for stress intensity factors of homogeneous plates. Computer Methods in Applied Mechanics and Engineering, 321, 427-454.
Boulenouar, A., Benseddiq, N., Mazari, M., & Benamara, N. (2014). FE model for linear-elastic mixed mode loading: estimation of SIFs and crack propagation. Journal of Theoretical and Applied Mechanics, 52.
Cooke, M. L., & Pollard, D. D. (1996). Fracture propagation paths under mixed mode loading within rectangular blocks of polymethyl methacrylate. Journal of Geophysical Research: Solid Earth, 101(B2), 3387-3400.
Dehghany, M., Saeidi Googarchin, H., & Aliha, M. R. M. (2017). The role of first non‐singular stress terms in mixed mode brittle fracture of V‐notched components: an experimental study. Fatigue & Fracture of Engineering Materials & Structures, 40(4), 623-641.
Duarte, C. A., & Oden, J. T. (1996). H‐p clouds—an h‐p meshless method. Numerical Methods for Partial Differential Equations: An International Journal, 12(6), 673-705.
Guo, L., Xiang, J., Latham, J. P., & Izzuddin, B. (2016). A numerical investigation of mesh sensitivity for a new three-dimensional fracture model within the combined finite-discrete element method. Engineering Fracture Mechanics, 151, 70-91.
Khan, S. M., & Khraisheh, M. K. (2000). Analysis of mixed mode crack initiation angles under various loading conditions. Engineering Fracture Mechanics, 67(5), 397-419.
Khan, S. M., & Khraisheh, M. K. (2004). A new criterion for mixed mode fracture initiation based on the crack tip plastic core region. International Journal of Plasticity, 20(1), 55-84.
Lan, M., Waisman, H., & Harari, I. (2013). A High‐order extended finite element method for extraction of mixed‐mode strain energy release rates in arbitrary crack settings based on Irwin's integral. International Journal for Numerical Methods in Engineering, 96(12), 787-812.
Liu, Y. J., Li, Y. X., & Xie, W. (2017). Modeling of multiple crack propagation in 2-D elastic solids by the fast multipole boundary element method. Engineering Fracture Mechanics, 172, 1-16.
Matvienko, Y. G. (2012). Maximum average tangential stress criterion for prediction of the crack path. International Journal of Fracture, 176(1), 113-118.
Miller, E. E., Sutton, M. A., Deng, X., Watts, H., Reynolds, A. P., Ke, X., & Schreier, H. W. (2015). Experimental and predicted crack paths for Al-2024-T351 under mixed-mode I/II fatigue. In Fracture, Fatigue, Failure, and Damage Evolution, Volume 5 (pp. 11-20). Springer, Cham.
Mirsayar, M. M., Aliha, M. R. M., & Samaei, A. T. (2014). On fracture initiation angle near bi-material notches–Effects of first non-singular stress term. Engineering fracture mechanics, 119, 124-131.
Mirsayar, M. M., Razmi, A., Aliha, M. R. M., & Berto, F. (2018). EMTSN criterion for evaluating mixed mode I/II crack propagation in rock materials. Engineering Fracture Mechanics, 190, 186-197.
Rao, B. N., & Rahman, S. (2001). A coupled meshless-finite element method for fracture analysis of cracks. International Journal of Pressure Vessels and Piping, 78(9), 647-657.
Razavi, S. M. J., Aliha, M. R. M., & Berto, F. (2018). Application of an average strain energy density criterion to obtain the mixed mode fracture load of granite rock tested with the cracked asymmetric four-point bend specimens. Theoretical and Applied Fracture Mechanics, 97, 419-425.
Rice, J. R. (1968). A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of applied mechanics, 35(2), 379-386.
Sabbagh-Yazdi, S. R., Farhoud, A., & Gharebaghi, S. A. (2018). Simulation of 2D linear crack growth under constant load using GFVM and two-point displacement extrapolation method. Applied Mathematical Modelling, 61, 650-667.
Sutton, M. A., Boone, M. L., Ma, F., & Helm, J. D. (2000). A combined modeling–experimental study of the crack opening displacement fracture criterion for characterization of stable crack growth under mixed mode I/II loading in thin sheet materials. Engineering Fracture Mechanics, 66(2), 171-185.
Tada, H., Paris, P., & Irwin, G. (2000). The analysis of cracks handbook. New York: ASME Press, 2, 1.
Varfolomeev, I., Burdack, M., Moroz, S., Siegele, D., & Kadau, K. (2014). Fatigue crack growth rates and paths in two planar specimens under mixed mode loading. International Journal of Fatigue, 58, 12-19.
Williams, M. L. (1957). The bending stress distribution at the base of a stationary crack. Trans. ASME, 79, 109-114.
Xie, D., & Waas, A. M. (2006). Discrete cohesive zone model for mixed-mode fracture using finite element analysis. Engineering fracture mechanics, 73(13), 1783-1796.
Zhang, R., & Guo, R. (2018). Determination of crack tip stress intensity factors by singular Voronoi cell finite element model. Engineering Fracture Mechanics, 197, 206-216.