How to cite this paper
Zeleke, M., Ageze, M., Batane, N & Dintwa, E. (2025). Exploring stress intensity factor computation: A parametric study using extended isogeometric analysis (XIGA).Engineering Solid Mechanics, 13(1), 125-140.
Refrences
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., Gu, L., & Lu, Y. Y. (1994, a). Fracture and crack growth by element free Galerkin methods. Modelling and Simulation in Materials Science and Engineering, 2(3A), 519.
Belytschko, T., Lu, Y. Y., & Gu, L. (1994, b). Element‐free Galerkin methods. International journal for numerical methods in engineering, 37(2), 229-256.
Bhardwaj, G., Singh, S. K., Patil, R. U., Godara, R. K., & Khanna, K. (2021). Thermo-elastic analysis of cracked functionally graded materials using XIGA. Theoretical and Applied Fracture Mechanics, 114, 103016.
Borden, M. J., Verhoosel, C. V., Scott, M. A., Hughes, T. J., & Landis, C. M. (2012). A phase-field description of dynamic brittle fracture. Computer Methods in Applied Mechanics and Engineering, 217, 77-95.
Bouhala, L., Shao, Q., Koutsawa, Y., Younes, A., Núñez, P., Makradi, A., & Belouettar, S. (2013). An XFEM crack-tip enrichment for a crack terminating at a bi-material interface. Engineering Fracture Mechanics, 102, 51-64.
Ching, H. K., & Yen, S. C. (2005). Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Composites Part B: Engineering, 36(3), 223-240.
De Luycker, E., Benson, D. J., Belytschko, T., Bazilevs, Y., & Hsu, M. C. (2011). X‐FEM in isogeometric analysis for linear fracture mechanics. International Journal for Numerical Methods in Engineering, 87(6), 541-565.
Fang, W., Zhang, J., Yu, T., & Bui, T. Q. (2021). Analysis of thermal effect on buckling of imperfect FG composite plates by adaptive XIGA. Composite Structures, 275, 114450.
Ghorashi, S. S., Valizadeh, N., & Mohammadi, S. (2012). Extended isogeometric analysis for simulation of stationary and propagating cracks. International Journal for Numerical Methods in Engineering, 89(9), 1069-1101.
Grifith, A. A. (1920). The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. Lond., A, 221, 163.
Gu, J., Yu, T., Tanaka, S., Qiu, L., & Bui, T. Q. (2019). Adaptive orthotropic XIGA for fracture analysis of composites. Composites Part B: Engineering, 176, 107259.
Gu, Y., Wang, W., Zhang, L. C., & Feng, X. Q. (2011). An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields. Engineering Fracture Mechanics, 78(1), 175-190.
Hughes, T. J., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer methods in applied mechanics and engineering, 194(39-41), 4135-4195.
Irwin, G. R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate.
Jameel, A., & Harmain, G. A. (2019). Extended iso-geometric analysis for modeling three-dimensional cracks. Mechanics of Advanced Materials and Structures, 26(11), 915-923.
Kastratović, G., Vidanović, N., Grbović, A., & Rašuo, B. (2018). Approximate determination of stress intensity factor for multiple surface cracks. FME transactions, 46(1), 39-45.
Lee, S. H., Kim, K. H., & Yoon, Y. C. (2016). Particle difference method for dynamic crack propagation. International Journal of Impact Engineering, 87, 132-145.
Liu, W. K., Jun, S., & Zhang, Y. F. (1995). Reproducing kernel particle methods. International journal for numerical methods in fluids, 20(8‐9), 1081-1106.
Lu, Y. Y., Belytschko, T., & Gu, L. (1994). A new implementation of the element free Galerkin method. Computer methods in applied mechanics and engineering, 113(3-4), 397-414.
Menk, A., & Bordas, S. P. (2011). Crack growth calculations in solder joints based on microstructural phenomena with X-FEM. Computational Materials Science, 50(3), 1145-1156.
Miehe, C., Hofacker, M., & Welschinger, F. (2010, a). A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 199(45-48), 2765-2778.
Miehe, C., Welschinger, F., & Hofacker, M. (2010, b). Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations. International journal for numerical methods in engineering, 83(10), 1273-1311.
Moës, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. International journal for numerical methods in engineering, 46(1), 131-150.
Nguyen, V. P., Anitescu, C., Bordas, S. P., & Rabczuk, T. (2015). Isogeometric analysis: an overview and computer implementation aspects. Mathematics and Computers in Simulation, 117, 89-116.
Pais, M. J. (2011). Variable amplitude fatigue analysis using surrogate models and exact XFEM reanalysis. University of Florida.
Rabczuk, T., & Belytschko, T. (2004). Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International journal for numerical methods in engineering, 61(13), 2316-2343.
Shoheib, M. M. (2023). Stress intensity factor and fatigue life evaluation for important points of semi-elliptical cracks in welded pipeline by Bezier extraction based XIGA and new correlation model. Engineering Analysis with Boundary Elements, 155, 264-280.
Sih, G. C. (1973). Handbook of stress-intensity factors. Lehigh University, Institute of Fracture and Solid Mechanics.
Singh, I. V., Mishra, B. K., Bhattacharya, S., & Patil, R. U. (2012). The numerical simulation of fatigue crack growth using extended finite element method. International Journal of Fatigue, 36(1), 109-119.
Tada, H., Paris, P. C., & Irwin, G. R. (2000). The stress analysis of cracks Handbook (3rd ed.), ASME Press, New York.
Yan, X. (2007). Rectangular tensile sheet with single edge crack or edge half-circular-hole crack. Engineering Failure Analysis, 14(7), 1406-1410.
Yang, H. S., Dong, C. Y., Qin, X. C., & Wu, Y. H. (2020). Vibration and buckling analyses of FGM plates with multiple internal defects using XIGA-PHT and FCM under thermal and mechanical loads. Applied Mathematical Modelling, 78, 433-481.
Zeleke, M., Dintwa, E., & Nwaigwe, K. (2021). Stress intensity factor computation of inclined cracked tension plate using XFEM. Engineering Solid Mechanics, 9(4), 363-376.
Zhong, S., Jin, G., Ye, T., & Chen, Y. (2024). A 3D-XIGA rotating cracked model for vibration analysis of blades. International Journal of Mechanical Sciences, 261, 108700.
Belytschko, T., Gu, L., & Lu, Y. Y. (1994, a). Fracture and crack growth by element free Galerkin methods. Modelling and Simulation in Materials Science and Engineering, 2(3A), 519.
Belytschko, T., Lu, Y. Y., & Gu, L. (1994, b). Element‐free Galerkin methods. International journal for numerical methods in engineering, 37(2), 229-256.
Bhardwaj, G., Singh, S. K., Patil, R. U., Godara, R. K., & Khanna, K. (2021). Thermo-elastic analysis of cracked functionally graded materials using XIGA. Theoretical and Applied Fracture Mechanics, 114, 103016.
Borden, M. J., Verhoosel, C. V., Scott, M. A., Hughes, T. J., & Landis, C. M. (2012). A phase-field description of dynamic brittle fracture. Computer Methods in Applied Mechanics and Engineering, 217, 77-95.
Bouhala, L., Shao, Q., Koutsawa, Y., Younes, A., Núñez, P., Makradi, A., & Belouettar, S. (2013). An XFEM crack-tip enrichment for a crack terminating at a bi-material interface. Engineering Fracture Mechanics, 102, 51-64.
Ching, H. K., & Yen, S. C. (2005). Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Composites Part B: Engineering, 36(3), 223-240.
De Luycker, E., Benson, D. J., Belytschko, T., Bazilevs, Y., & Hsu, M. C. (2011). X‐FEM in isogeometric analysis for linear fracture mechanics. International Journal for Numerical Methods in Engineering, 87(6), 541-565.
Fang, W., Zhang, J., Yu, T., & Bui, T. Q. (2021). Analysis of thermal effect on buckling of imperfect FG composite plates by adaptive XIGA. Composite Structures, 275, 114450.
Ghorashi, S. S., Valizadeh, N., & Mohammadi, S. (2012). Extended isogeometric analysis for simulation of stationary and propagating cracks. International Journal for Numerical Methods in Engineering, 89(9), 1069-1101.
Grifith, A. A. (1920). The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. Lond., A, 221, 163.
Gu, J., Yu, T., Tanaka, S., Qiu, L., & Bui, T. Q. (2019). Adaptive orthotropic XIGA for fracture analysis of composites. Composites Part B: Engineering, 176, 107259.
Gu, Y., Wang, W., Zhang, L. C., & Feng, X. Q. (2011). An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields. Engineering Fracture Mechanics, 78(1), 175-190.
Hughes, T. J., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer methods in applied mechanics and engineering, 194(39-41), 4135-4195.
Irwin, G. R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate.
Jameel, A., & Harmain, G. A. (2019). Extended iso-geometric analysis for modeling three-dimensional cracks. Mechanics of Advanced Materials and Structures, 26(11), 915-923.
Kastratović, G., Vidanović, N., Grbović, A., & Rašuo, B. (2018). Approximate determination of stress intensity factor for multiple surface cracks. FME transactions, 46(1), 39-45.
Lee, S. H., Kim, K. H., & Yoon, Y. C. (2016). Particle difference method for dynamic crack propagation. International Journal of Impact Engineering, 87, 132-145.
Liu, W. K., Jun, S., & Zhang, Y. F. (1995). Reproducing kernel particle methods. International journal for numerical methods in fluids, 20(8‐9), 1081-1106.
Lu, Y. Y., Belytschko, T., & Gu, L. (1994). A new implementation of the element free Galerkin method. Computer methods in applied mechanics and engineering, 113(3-4), 397-414.
Menk, A., & Bordas, S. P. (2011). Crack growth calculations in solder joints based on microstructural phenomena with X-FEM. Computational Materials Science, 50(3), 1145-1156.
Miehe, C., Hofacker, M., & Welschinger, F. (2010, a). A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 199(45-48), 2765-2778.
Miehe, C., Welschinger, F., & Hofacker, M. (2010, b). Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations. International journal for numerical methods in engineering, 83(10), 1273-1311.
Moës, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. International journal for numerical methods in engineering, 46(1), 131-150.
Nguyen, V. P., Anitescu, C., Bordas, S. P., & Rabczuk, T. (2015). Isogeometric analysis: an overview and computer implementation aspects. Mathematics and Computers in Simulation, 117, 89-116.
Pais, M. J. (2011). Variable amplitude fatigue analysis using surrogate models and exact XFEM reanalysis. University of Florida.
Rabczuk, T., & Belytschko, T. (2004). Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International journal for numerical methods in engineering, 61(13), 2316-2343.
Shoheib, M. M. (2023). Stress intensity factor and fatigue life evaluation for important points of semi-elliptical cracks in welded pipeline by Bezier extraction based XIGA and new correlation model. Engineering Analysis with Boundary Elements, 155, 264-280.
Sih, G. C. (1973). Handbook of stress-intensity factors. Lehigh University, Institute of Fracture and Solid Mechanics.
Singh, I. V., Mishra, B. K., Bhattacharya, S., & Patil, R. U. (2012). The numerical simulation of fatigue crack growth using extended finite element method. International Journal of Fatigue, 36(1), 109-119.
Tada, H., Paris, P. C., & Irwin, G. R. (2000). The stress analysis of cracks Handbook (3rd ed.), ASME Press, New York.
Yan, X. (2007). Rectangular tensile sheet with single edge crack or edge half-circular-hole crack. Engineering Failure Analysis, 14(7), 1406-1410.
Yang, H. S., Dong, C. Y., Qin, X. C., & Wu, Y. H. (2020). Vibration and buckling analyses of FGM plates with multiple internal defects using XIGA-PHT and FCM under thermal and mechanical loads. Applied Mathematical Modelling, 78, 433-481.
Zeleke, M., Dintwa, E., & Nwaigwe, K. (2021). Stress intensity factor computation of inclined cracked tension plate using XFEM. Engineering Solid Mechanics, 9(4), 363-376.
Zhong, S., Jin, G., Ye, T., & Chen, Y. (2024). A 3D-XIGA rotating cracked model for vibration analysis of blades. International Journal of Mechanical Sciences, 261, 108700.