[1] M. Bentahar, H. Benzaama, N. Mahmoudin, Numerical Modeling of the Evolution of the Strain energy ALLSE of the Crack Propagation by the X-FEM Method. Review of Renewable Materials and Energies, 5(2), 2021: 24-31.
https://www.asjp.cerist.dz/en/article/167392
[2] G.-B. Lee, S.-H. Park, Y.-Y. Jang, N.-S Huh, S.-H Park, N.-H. Park, J. Park, Development of Automatic Crack Growth Simulation Program Based on Finite Element Analysis. Applied Sciences, 12(6), 2022: 3075. 
https://doi.org/10.3390/app12063075
[3] Z.A. Alkaissi, Modelling of Crack Propagation in Flexible Pavement Using X-FEM Method. IOP Conference Series: Earth and Environmental Science, 961, 2022: 012014. https://doi.org/10.1088/17551315/961/1/012014
[4] H. Laribou, C. Qotni, Determination of the Stress Intensity Factor with an Empirical Approach for Circular and Elliptical Cracked Sections. American Journal of Mechanical Engineering, 10(1), 2022: 9-16.
[5] S. El Fakkoussi, H. Moustabchir, A. Elkhalfi, C.I. Pruncu, Computation of the stress intensity factor KI for external longitudinal semi-elliptic cracks in the pipelines by FEM and XFEM methods. International Journal on Interactive Design and Manufacturing (IJIDeM), 13, 2019: 545-555. https://doi.org/10.1007/s12008-018-0517-1
[6] A.M. Alshoaibi, Y.A. Fageehi, 2D finite element simulation of mixed mode fatigue crack propagation for CTS specimen. Journal of Materials Research and Technology, 9(4), 2020: 7850-7861. https://doi.org/10.1016/j.jmrt.2020.04.083
[7] M.A. Bouaziz, J. Marae-Djouda, M. Zouaoui, J. Gardan, F. Hild, Crack growth measurement and J-integral evaluation of additively manufactured polymer using digital image correlation and FE modelling. Fatigue and Fracture of Engineering Materials and Structures, 44(5), 2021: 1318-1335. https://doi.org/10.1111/ffe.13431
[8] A. Shafiei, Dynamic crack propagation in plates weakened by inclined cracks: an investigation based on peridynamics. Frontiers of Structural and Civil Engineering,12(4), 2018: 527-535. https://doi.org/10.1007/s11709-018-0450-1
[9] M. Bentahar, H. Benzaama, Numerical Simulation of the Synthetic Strain Energy and Crack Characterization Parameters Using the FEM Method of a Two-Dimensional Multi-Position Model. Selcukuniversity Journal of Engineering Sciences, 22(3), 2023: 100-109.
[10] W. Tu, J. Deng, H. Tang, D. Dong, Experimental study on the biaxial non- proportional low-cycle fatigue crack growth behavior of hull inclined cracked plate. 31^st International Ocean and Polar Engineering Conference, June 2021, Rhodes, Greece, ISOPE-I-21-4137.
[11] F. Habib, L. Sorelli, M. Fafard, Full thermo-mechanical coupling using eXtended finite element method in quasi-transient crack propagation. Advanced Modeling and Simulation in Engineering Sciences, 5, 2018: 18.
https://doi.org/10.1186/s40323-018-0112-9
[12] M. Bentahar, H. Benzaama, Numerical simulation of two-dimensional crack propagation using stretching finite element method by Abaqus. Tribology and Materials, 1(4), 2022: 145-149. https://doi.org/10.46793/tribomat.2022.018
[13] M. Bentahar, H. Benzaama, M. Bentoumi, M. Mokhtari, A new automated stretching finite element method for 2D crack propagation. Journal of Theoretical and Applied Mechanics, 55(3), 2017: 869-881. https://doi.org/10.15632/jtam-pl.55.3.869
[14] P. Paris, F. Erdogan, A critical analysis of crack propagation laws. Journal of Basic Engineering, 85(4), 1963: 528-534. https://doi.org/10.1115/1.3656900
[15] H. Tada, P.C. Paris, G.R. Irwin, The Stress Analysis of Cracks Handbook. American Society of Mechanical Engineers, 2000. https://doi.org/10.1115/1.801535
[16] F. Erdogan, G.C. Sih, On the crack extension in plates under plane loading and transverse shear. Journal of Basic Engineering, 85, 1963: 519-527. https://doi.org/10.1115/1.3656897
[17] F. Saverio, Phenomenon of plasticity-induced crack closure during the propagation of a fatigue crack in a 304L stainless steel. National Engineering School of Mechanical and Aeronautical Engineering, PhD thesis, Chasseneuil-du-Poitou, France, 2014. https://theses.fr/2014ESMA0018
[18] J.R. Rice, A path independent integral and the approximate analysis of strain concentrations by notches and cracks. Journal of Applied Mechanics, 35(2), 1968: 379-386. https://doi.org/10.1115/1.3601206
[19] H.D. Bui, Duality and symmetry lost in solid mechanics. Comptes Rendus Mécanique, 336(1-2), 2008: 12-23.
https://doi.org/10.1016/j.crme.2007.11.018
[20] Q.S. Nguyen, C. Stolz, G. Debruyne, Energy methods in fracture mechanics: stability, bifurcation and second variations. European Journal of Mechanics – A/Solids, 9(2), 1990, 157-173.
[21] P. Destuynder, P.E.M. Djaoua, L. Chesnay, J.C. Nedelec, Sur une Interprétation Mathématique de l’Intégrale de Rice en Théorie de la Rupture Fragile. Mathematical Methods in the Applied Sciences, 3(1), 1981:70-87.
https://doi.org/10.1002/mma.1670030106
[22] M. Bentahar, ALLDMD dissipation energy analysis by the method extended finite elements of a 2D cracked structure of an elastic linear isotropic homogeneous material. Journal of Electronics, Computer Networking and Applied Mathematics, 3(2), 2023: 1-8. https://doi.org/10.55529/jecnam.32.1.8
[23] M. Bentahar, Fatigue analysis of an inclined crack propagation problem by the X-FEM method. International Journal of Applied and Structural Mechanics, 3(4), 2023: 23- 31. https://doi.org/10.55529/ijasm.34.23.31
[24] M. Bentahar, Numerical study of a centred crack on an elastoplastic material by the FEM method. Tribology and Materials, 2(3), 2023: 108-113. https://doi.org/10.46793/tribomat.2023.011