Refrences:
1.Borri, A., Castori, G., and Corradi, M. Intrados strengthening of brick masonry arches with composite materials", Composites Part B: Eng., 42, pp. 1164- 1172 (2011).
2. Tao, Y., Stratford, T.J., and Chen, J.F. Behaviour of a masonry arch bridge repaired using _bre-reinforced polymer composites", Eng. Struct., 33, pp. 1594-1606 (2011).
3. Chen, H., Zhou, J., Fan, H., et al. Dynamic responses of buried arch structure subjected to subsurface localized impulsive loading: Experimental study", Int. J. Impact Eng., 65, pp. 89-101 (2014). 4. Hamed, E., Chang, Z.T., and Rabinovitch, O. Strengthening of reinforced concrete arches with externally bonded composite materials: Testing and analysis", J. Composites Construc., 19, pp. 04014031 (2015). 5. Dagher, H.J., Bannon, D.J., Davids, W.G., et al. Bending behavior of concrete-_lled tubular FRP arches for bridge structures", Construc. Building Mater., 37, pp. 432-439 (2012). 6. Zhang, X., Wang, P., Jiang, M., et al. CFRP strengthening reinforced concrete arches: Strengthening methods and experimental studies", Composite Struct., 131, pp. 852-867 (2015). 7. Feenstra, P.H. and de Borst, R. A composite plasticity model for concrete", Int. J. Solids Struct., 33, pp. 707-730 (1996). 8. _Cervenka, J. and Papanikolaou, V.K. Three dimensional combined fracture-plastic material model for concrete", Int. J. Plasticity, 24, pp. 2192-2220 (2008). 9. Khoei, A.R. and Azami, A.R. A single cone-cap plasticity with an isotropic hardening rule for powder materials", Int. J. Mech. Sciences, 47, pp. 94-109 (2005). 10. DorMohammadi, H. and Khoei, A.R. A threeinvariant cap model with isotropic-kinematic hardening rule and associated plasticity for granular materials", Int. J. Solids Struct., 45, pp. 631-656 (2008). 11. Ba_zant, Z.P. and O_zbolt, J. Nonlocal microplane model for fracture, damage, and size e_ect in structures", J. Eng. Mech., 116, pp. 2485-2505 (1990). 12. Voyiadjis, G.Z. and Abu-Lebdeh, T.M. Damage model for concrete using bounding surface concept", J. Eng. Mech., 119, pp. 1865-1885 (1993). 13. Lubliner, J., Oliver, J., Oller, S., et al. A plasticdamage model for concrete", Int. J. Solids Struct., 25, pp. 299-326 (1989). 14. Yazdani, S. and Schreyer, H.L. Combined plasticity and damage mechanics model for plain concrete", J. Eng. Mech., 116, pp. 1435-1450 (1990). 15. Kattan, P.I. and Voyiadjis, G.Z. A coupled theory of damage mechanics and _nite strain elasto-plasticity - I. Damage and elastic deformations", Int. J. Eng. Science, 28, pp. 421-435 (1990). 16. Kattan, P.I. and Voyiadjis, G.Z. A coupled theory of damage mechanics and _nite strain elasto-plasticity - II. Damage and _nite strain plasticity", Int. J. Eng. Science, 28, pp. 505-524 (1990). 17. Lee, J. and Fenves, G.L. Plastic-damage model for cyclic loading of concrete structures", J. Eng. Mech., 124, pp. 892-900 (1998). 18. Faria, R., Oliver, J., and Cervera, M. A strain-based plastic viscous-damage model for massive concrete structures", Int. J. Solids Struct., 35, pp. 1533-1558 (1998). 19. Salari, M.R., Saeb, S., Willam, K.J., et al. A coupled elastoplastic damage model for geomaterials", Comput. Meth. Applied Mech. Eng., 193, pp. 2625-2643 (2004). 20. Grassl, P. and Jir_asek, M. Damage-plastic model for concrete failure", Int. J. Solids Struct., 43, pp. 7166- 7196 (2006). 21. Nguyen, G.D. and Korsunsky, A.M. Damageplasticity modelling of concrete: calibration of parameters using separation of fracture energy", Int. J. Fracture, 139, pp. 325-332 (2006). 2132 T. Ahmadpour et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 2123{2132 22. Nguyen, G.D. and Houlsby, G.T. A coupled damageplasticity model for concrete based on thermodynamic principles: Part I: model formulation and parameter identi_cation", Int. J. Numer. Analy. Meth. Geomech., 32, pp. 353-389 (2008). 23. Nguyen, G.D. and Houlsby, G.T. A coupled damageplasticity model for concrete based on thermodynamic principles: Part II: non-local regularization and numerical implementation", Int. J. Numer. Analy. Meth. Geomech., 32, pp. 391-413 (2008). 24. Moslemi, H. and Khoei, A.R. 3D modeling of damage growth and crack initiation using adaptive _nite element technique", Scientia Iranica, Trans. A., J. Civil Eng., 17, pp. 372-386 (2010). 25. Khoei, A.R., Eghbalian, M., Azadi, H., et al. Numerical simulation of ductile crack growth under cyclic and dynamic loading with a damage-viscoplasticity model", Eng. Fracture Mech., 99, pp. 169-190 (2013). 26. Broumand, P. and Khoei, A.R. The extended _nite element method for large deformation ductile fracture problems with a non-local damage-plasticity model", Eng. Fracture Mech., 112, pp. 97-125 (2013). 27. Broumand, P. and Khoei, A.R. X-FEM modeling of dynamic ductile fracture problems with a nonlocal damage-viscoplasticity model", Finite Elements Anal. Design, 99, pp. 49-67 (2015). 28. Khoei, A.R., Extended Finite Element Method: Theory and Applications, John Wiley (2015). 29. Khoei, A.R., Moslemi, H., Ardakany, K.M., et al. Modeling of cohesive crack growth using an adaptive mesh re_nement via the modi_ed-SPR technique", Int. J. Fracture, 159, pp. 21-41 (2009). 30. Khoei, A.R., Moslemi, H., and Shari_, M. Threedimensional cohesive fracture modeling of non-planar crack growth using adaptive FE technique", Int. J. Solids Struct., 49, pp. 2334-2348 (2012). 31. Turon, A., Camanho, P.P., Costa, J., et al. A damage model for the simulation of delamination in advanced composites under variable-mode loading", Mech. Mater., 38, pp. 1072-1089 (2006). 32. Gopalaratnam, V. and Shah, S.P. Softening response of plain concrete in direct tension", ACI Mater. J., 82, pp. 310-323 (1985). 33. Au, C. and Buyukozturk, O. Peel and shear fracture characterization of debonding in FRP plated concrete a_ected by moisture", J. Composites Construc., 10, pp. 35-47 (2006). 34. Moradi, H., Khaloo, A., Shekarchi, M., and Kazemian, A. E_ect of glass _ber-reinforced polymer on exural strengthening of RC arches", Scientia Iranica, Transactions A, 26(4), pp. 2299-2309 (2019).