[2] Alexander J., An approximate analysis of the collapse of thin cylindrical shells under axial loading, The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 13, No. 1, pp. 10-15, 1960.
[3] Abramowicz W. and Jones N., Dynamic progressive buckling of circular and square tubes, International Journal of Impact Engineering, Vol. 4, No. 4, pp. 243-270, 1986.
[4] Nia A. A. and Hamedani J. H., Comparative analysis of energy absorption and deformations of thin walled tubes with various section geometries, Thin-Walled Structures, Vol. 48, No. 12, pp. 946-954, 2010.
[5] Shariati M. and Rokhi M. M., Numerical and Experimental Investigations on Buckling of Steel Cylindrical Shells with Elliptical Cutout Subject to Axial Compression, Thin-Walled Structures, Vol. 46, pp. 1251– 1261, 2008.
[6] Shariati M. and Rokhi M. M., Buckling of Steel Cylindrical Shells with an Elliptical Cutout, International Journal of Steel Structures, Vol. 10, No 2, pp. 193-205, 2010.
[7] Shariati M., Sedighi M., Saemi J., Eipakchi H., Allahbakhsh H., Numerical and experimental investigation on ultimate strength of cracked cylindrical shells subjected to combined loading, Mechanika, Vol. 4, No. 84, pp. 12-19, 2010.
[9] Allahbakhsh H. R., Shariati M. and Sedighi M., Effect of stiffeners on crashworthiness of square aluminium columns considering damage evolution, J. Cent. South Univ,Vol. 20, pp. 599−607, 2013.
[13] B. Wang B. and Lu G., Mushrooming of circular tubes under dynamic axial loading, Thin-walled structures, Vol. 40, No. 2, pp. 167-182, 2002.
[14] Mokhtarnezhad F., Salehghaffari S. and Tajdari M., Improving the crashworthiness characteristics of cylindrical tubes subjected to axial compression by cutting wide grooves from their outer surface, International Journal of Crashworthiness, Vol. 14, No. 6, pp. 601-611, 2009.
[15] Salehghaffari S., Tajdari M., Panahi M. and Mokhtarnezhad F., Attempts to improve energy absorption characteristics of circular metal tubes subjected to axial loading, Thin-Walled Structures, Vol. 48, No. 6, pp. 379-390, 2010.
[16] Tarlochan F., Samer F., Hamouda A., Ramesh S. and Khalid K., Design of thin wall structures for energy absorption applications: enhancement of crashworthiness due to axial and oblique impact forces, Thin-Walled Structures, Vol. 71, pp. 7-17, 2013.
[17] Hanssen A., Hopperstad O., Langseth M. and Ilstad H., Validation of constitutive models applicable to aluminium foams, International journal of mechanical sciences, Vol. 44, No. 2, pp. 359-406, 2002.
[18] Reyes A., Langseth M. and Hopperstad O., Square aluminum tubes subjected to oblique loading, International Journal of Impact Engineering, Vol. 28, No. 10, pp. 1077-1106, 2003.
[19] Børvik T., Hopperstad O., Reyes A., Langseth M., Solomos G. and Dyngeland T., Empty and foam-filled circular aluminium tubes subjected to axial and oblique quasistatic loading, International journal of crashworthiness, Vol. 8, No. 5, pp. 481-494, 2003.
[20] Santosa S. P., Wierzbicki T., Hanssen A. G. and Langseth M., Experimental and numerical studies of foam-filled sections, International Journal of Impact Engineering, Vol. 24, No. 5, pp. 509-534, 2000.
[21] Kavi H., Toksoy A. K. and Guden M., Predicting energy absorption in a foam-filled thin-walled aluminum tube based on experimentally determined strengthening coefficient, Materials & design, Vol. 27, No. 4, pp. 263-269, 2006.
[26] Peirs J., Verleysen P., Van Paepegem W. and Degrieck J., Determining the stress–strain behaviour at large strains from high strain rate tensile and shear experiments, International Journal of Impact Engineering, Vol. 38, No. 5, pp. 406-415, 2011.
[27] Gurson A. L., Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media, Journal of engineering materials and technology, Vol. 99, No. 1, pp. 2-15, 1977.
[28] Tvergaard V. and Needleman A., Analysis of the cup-cone fracture in a round tensile bar, Acta metallurgica, Vol. 32, No. 1, pp. 157-169, 1984.
[29] Østby E., Thaulow C. and Zhang Z., Numerical simulations of specimen size and mismatch effects in ductile crack growth–Part I: Tearing resistance and crack growth paths, Engineering fracture mechanics, Vol. 74, No. 11, pp. 1770-1792, 2007.
[30] Li H., Fu M., Lu J., Yang H., Ductile fracture: experiments and computations, International journal of plasticity, Vol. 27, No. 2, pp. 147-180, 2011.
[31] Rousselier G., Dissipation in porous metal plasticity and ductile fracture, Journal of the Mechanics and Physics of Solids, Vol. 49, No. 8, pp. 1727-1746, 2001.
[32] Lorentz E., Besson J. and Cano V., Numerical simulation of ductile fracture with the Rousselier constitutive law, Computer Methods in Applied Mechanics and Engineering, Vol. 197, No. 21, pp. 1965-1982, 2008.
[33] Mirza M., Barton D. and Church P., The effect of stress triaxiality and strain-rate on the fracture characteristics of ductile metals, Journal of materials science, Vol. 31, No. 2, pp. 453-461, 1996.
[34] Needleman A. and Tvergaard V., An analysis of ductile rupture in notched bars, Journal of the Mechanics and Physics of Solids, Vol. 32, No. 6, pp. 461-490, 1984.
[35] Hancock J. and Mackenzie A., On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states, Journal of the Mechanics and Physics of Solids, Vol. 24, No. 2-3, pp. 147-160, 1976.
[36] Zhu H., Qin C., Wang J. Q. and Qi F. J., Characterization and simulation of mechanical behavior of 6063 aluminum alloy thin-walled tubes, Advanced Materials Research, Vol. 197-198, pp. 1500-1508, 2011.
[37] Tvergaard V., Influence of void nucleation on ductile shear fracture at a free surface, Journal of the Mechanics and Physics of Solids, Vol. 30, No. 6, pp. 399-425, 1982.
[38] Tvergaard V., On localization in ductile materials containing spherical voids, International Journal of Fracture, Vol. 18, No. 4, pp. 237-252, 1982.
[40] Xu F., Zhao S. and Han X., Use of a modified Gurson model for the failure behaviour of the clinched joint on Al6061 sheet, Fatigue & Fracture of Engineering Materials & Structures, Vol. 37, No. 3, pp. 335-348, 2014.
[41] Nahshon K. and Hutchinson J., Modification of the Gurson model for shear failure, European Journal of Mechanics-A/Solids, Vol. 27, No. 1, pp. 1-17, 2008.
[42] Guo J., Zhao S., Murakami R.-i. and Zang S., Experimental and numerical investigation for ductile fracture of Al-alloy 5052 using modified Rousselier model, Computational Materials Science, Vol. 71, pp. 115-123, 2013
[43] Zhao R., Zhao S., Guo J., Zhong B. and Li J., Experimental and numerical investigation on ductile fracture mechanism of aluminium alloy using new modified model, Materials Science and Technology, Vol. 31, No. 3, pp. 303-309, 2015.