[1] Valko, P., & Economides, M. J. (1995). “Hydraulic fracture mechanics” (Vol. 28, p. 206). Chichester: Wiley.
[2] Yao, Y., Gosavi, S. V., Searles, K. H., & Ellison, T. K. (2010, January). “Cohesive fracture mechanics based analysis to model ductile rock fracture”. In 44th US Rock Mechanics Symposium and 5th US-Canada Rock Mechanics Symposium. American Rock Mechanics Association.
[3] Ortiz, M., & Pandolfi, A. (1999). “Finite‐deformation irreversible cohesive elements for three‐dimensional crack‐ propagation analysis”. International journal for numerical methods in engineering, 44(9), 1267-1282.
[4] ABAQUS, “6.14 documentation,” Dassault Systemes Simulia Corporation, 2014.
[5] Zielonka, M. G., Searles, K. H., Ning, J., & Buechler, S. R. (2014, May). “Development and validation of fully-coupled hydraulic fracturing simulation capabilities”. In Proceedings of the SIMULIA community conference, SCC2014 (pp. 19-21).
[6] Khoei, A. R. (2014). “Extended finite element method: theory and applications”. John Wiley & Sons.
[7] Haddad, M., & Sepehrnoori, K. (2015, April). “Integration of XFEM and CZM to model 3D multiple-stage hydraulic fracturing in quasi-brittle shale formations: solution-dependent propagation direction”. In Proceedings of the AADE National Technical Conference and Exhibition, AADE2015, San Antonio, Texas, 8-9 April 2015.
[8] 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.
[9] 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.
[10] Daux, C., Moës, N., Dolbow, J., Sukumar, N., & Belytschko, T. (2000). “Arbitrary branched and intersecting cracks with the extended finite element method”. International journal for numerical methods in engineering, 48(12), 1741-1760.
[11] Sukumar, N., Moës, N., Moran, B., & Belytschko, T. (2000). “Extended finite element method for three‐dimensional crack modelling”. International journal for numerical methods in engineering, 48(11), 1549-1570.
[12] Moës, N., & Belytschko, T. (2002). “Extended finite element method for cohesive crack growth”. Engineering fracture mechanics, 69(7), 813-833.
[13] Budyn, E., Zi, G., Moës, N., & Belytschko, T. (2004). “A method for multiple crack growth in brittle materials without remeshing”. International journal for numerical methods in engineering, 61(10), 1741-1770.
[14] Zi, G., Song, J. H., Budyn, E., Lee, S. H., & Belytschko, T. (2004). “A method for growing multiple cracks without remeshing and its application to fatigue crack growth”. Modelling and Simulation in Materials Science and Engineering, 12(5), 901.
[15] Khoei, A. R., Moallemi, S., & Haghighat, E. (2012). “Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique”. Engineering Fracture Mechanics, 96, 701-723.
[16] Watanabe, N., Wang, W., Taron, J., Görke, U. J., & Kolditz, O. (2012). “Lower‐dimensional interface elements with local enrichment: application to coupled hydro‐mechanical problems in discretely fractured porous media”. International Journal for Numerical Methods in Engineering, 90(8), 1010-1034.
[17] Gordeliy, E., & Peirce, A. (2013). “Coupling schemes for modeling hydraulic fracture propagation using the XFEM”. Computer Methods in Applied Mechanics and Engineering, 253, 305-322.
[18] Mohammadnejad, T., & Khoei, A. R. (2013). “An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies”. Computational Mechanics, 51(3), 327-345.
[19] Mohammadnejad, T., & Khoei, A. R. (2013). “An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model”. Finite Elements in Analysis and Design, 73, 77-95.
[20] Sarris, E., & Papanastasiou, P. (2012). “Modeling of hydraulic fracturing in a poroelastic cohesive formation”. International Journal of Geomechanics, 12(2), 160-167.
[21] Carrier, B., & Granet, S. (2012). “Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model”. Engineering fracture mechanics, 79, 312-328.
[22] Mohammadnejad, T., & Khoei, A. R. (2013). “Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method”. International Journal for Numerical and Analytical Methods in Geomechanics, 37(10), 1247-1279.
[23] Khoei, A. R., & Vahab, M. (2014). “A numerical contact algorithm in saturated porous media with the extended finite element method”. Computational Mechanics, 54(5), 1089-1110.
[24] Mohammadnejad, T., & Andrade, J. E. (2016). “Numerical modeling of hydraulic fracture propagation, closure and reopening using XFEM with application to in‐situ stress estimation”. International Journal for Numerical and Analytical Methods in Geomechanics, 40(15), 2033-2060.
[25] Khodabakhshnejad, A. (2016). “An extended finite element method based modeling of hydraulic fracturing” (Doctoral dissertation, University of Southern California).
[26] Song, J. H., Areias, P. M., & Belytschko, T. (2006). “A method for dynamic crack and shear band propagation with phantom nodes”. International Journal for Numerical Methods in Engineering, 67(6), 868-893.
[27] Fisher, M. K., Heinze, J. R., Harris, C. D., Davidson, B. M., Wright, C. A., & Dunn, K. P. (2004). “Optimizing Horizontal Completion Techniques in the Barnett Shale Using Microseismic Fracture Mapping”. Paper SPE 90051 presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 26–29 September.
[28] Lolon, E., Cipolla, C., Weijers, L., Hesketh, R. E., & Grigg, M. W. (2009, January). “Evaluating horizontal well placement and hydraulic fracture spacing/conductivity in the Bakken Formation”, North Dakota. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.
[29] Cipolla, C. L., Lolon, E., Mayerhofer, M. J., & Warpinski, N. R. (2009, January). “Fracture design considerations in horizontal wells drilled in unconventional gas reservoirs”. In SPE Hydraulic Fracturing Technology Conference. Society of Petroleum Engineers.
[30] Chen, Z., Bunger, A. P., Zhang, X., & Jeffrey, R. G. (2009). “Cohesive zone finite element-based modeling of hydraulic fractures”. Acta Mechanica Solida Sinica, 22(5), 443-452.
[31] Sarris, E., & Papanastasiou, P. (2011). “The influence of the cohesive process zone in hydraulic fracturing modelling”. International Journal of Fracture, 167(1), 33-45.
[32] Osholake, T., Yilin Wang, J., & Ertekin, T. (2013). “Factors affecting hydraulically fractured well performance in the Marcellus shale gas reservoirs”. Journal of Energy Resources Technology, 135(1).
[33] Shin, D. H. (2013). “Simultaneous propagation of multiple fractures in a horizontal well”. Ph.D.thesis, University of Texas at Austin.
[34] Haddad*, M., & Sepehrnoori, K. (2014, August). “Simulation of multiple-stage fracturing in quasibrittle shale formations using pore pressure cohesive zone model”. In Unconventional Resources Technology Conference, Denver, Colorado, 25-27 August 2014 (pp. 1777-1792). Society of Exploration Geophysicists, American Association of Petroleum Geologists, Society of Petroleum Engineers.
[35] Hamidi, F., & Mortazavi, A. (2014). “A new three dimensional approach to numerically model hydraulic fracturing process”. Journal of Petroleum Science and Engineering, 124, 451-467.
[36] Haddad, M., & Sepehrnoori, K. (2015). “Simulation of hydraulic fracturing in quasi-brittle shale formations using characterized cohesive layer: Stimulation controlling factors”. Journal of Unconventional Oil and Gas Resources, 9, 65-83
[37] Yao, Y., Liu, L., & Keer, L. M. (2015). “Pore pressure cohesive zone modeling of hydraulic fracture in quasi-brittle rocks”. Mechanics of Materials, 83, 17-29.
[38] Wang, X., Liu, C., Wang, H., Liu, H., & Wu, H. (2016). “Comparison of consecutive and alternate hydraulic fracturing in horizontal wells using XFEM-based cohesive zone method”. Journal of Petroleum Science and Engineering, 143, 14-25.
[39] Wang, H. (2016). “Poro-elasto-plastic modeling of complex hydraulic fracture propagation: simultaneous multi-fracturing and producing well interference”. Acta Mechanica, 227(2), 507-525.
[40] Saberhosseini, S. E., Keshavarzi, R., & Ahangari, K. (2017). “A fully coupled three-dimensional hydraulic fracture model to investigate the impact of formation rock mechanical properties and operational parameters on hydraulic fracture opening using cohesive elements method”. Arabian Journal of Geosciences, 10(7), 157.
[41] Mehrgini, B., Memarian, H., Dusseault, M. B., Sheikhmali, R., Eshraghi, H., Ghavidel, A., ... & Badsar, A. (2017, August). “Hydraulic fracture geometry and geomechanical characteristics of carbonate reservoir rock”. In 51st US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association.
[42] Feng, Y., & Gray, K. E. (2017, August). “Modeling near-wellbore hydraulic fracture complexity using coupled pore pressure extended finite element method”. In 51st US rock mechanics/geomechanics symposium. American Rock Mechanics Association.
[43] Carrier, B., & Granet, S. (2012). “Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model”. Engineering fracture mechanics, 79, 312-328.
[44] Chen, Z. (2013, May). “An ABAQUS implementation of the XFEM for hydraulic fracture problems”. In ISRM International Conference for Effective and Sustainable Hydraulic Fracturing. International Society for Rock Mechanics and Rock Engineering.
[45] Barenblatt, G. I. (1959). “The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses”. Axially-symmetric cracks. Journal of Applied Mathematics and Mechanics, 23(3), 622-636.
[46] Barenblatt, G. I. (1962). “The mathematical theory of equilibrium cracks in brittle fracture”. Advances in applied mechanics, 7(1), 55-129.
[47] Hillerborg, A., Modéer, M., & Petersson, P. E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements”. Cement and concrete research, 6(6), 773-781.