Sub-Impact Phenomenon of Elasto-Plastic Free-Free Beam during a Strike

Authors: H. Rong, X. C. Yin, J. Yang, Y. N. Shen

Abstract:

Based on Rayleigh beam theory, the sub-impacts of a free-free beam struck horizontally by a round-nosed rigid mass is simulated by the finite difference method and the impact-separation conditions. In order to obtain the sub-impact force, a uniaxial compression elastic-plastic contact model is employed to analyze the local deformation field on contact zone. It is found that the horizontal impact is a complicated process including the elastic plastic sub-impacts in sequence. There are two sub-zones of sub-impact. In addition, it found that the elastic energy of the free-free beam is more suitable for the Poisson collision hypothesis to explain compression and recovery processes.

Keywords: beam, sub-impact, elastic-plastic deformation, finite difference method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328680

References:

[1] Jones N, Wierzbicki T. "Dynamic plastic failure of a free-free beam." International Journal of Impact Engineering, 1987, 6(3): 225-240.
[2] Q. Zhang, X. Wang, F. Huang, et al. "An experimental and numerical study of the dynamic response of a free-free aluminum beam under high velocity transverse impact." International Journal of Impact Engineering, 2009, 36(12): 1385-1393.
[3] X.C. Yin, Y. Qin, H. Zou, 2007. "Transient responses of repeated impact of a beam against a stop," Int. J. Solids Struct, 44(22-23): 7323-7339.
[4] Z.H. Liu, X.C. Yin, 2010. "Multiple elastic-plastic impacts of a variable cross-section beam struck by a round-nosed rigid mass in an impact course." Engineering Mechanics, 27(11): 244-249. (in Chinese)
[5] Melcher J´╝îXu X, Ramana A, 2008. "Multiple impact regimes in liquid environment dynamic atomic force microscopy," Appl. Phys. Lett., 93(9): 093111.
[6] Stoianovici D, Hurmuzlu Y, 1996. "A critical study of the applicability of rigid-body collision theory," ASME J. Appl. Mech., 63(2): 307-316.
[7] H. Shan, J.H. Su, Zhu J S, Xu L, 2007. "Three-dimensional modeling and simulation of a falling electronic device," ASME J. Comput. Nonlinear Dynam., 2(1): 22-31.
[8] J.L. Yang, F. Xi. "Experimental and theoretical study of free-free beam subjected to impact at any cross-section along its span. " International Journal of Impact Engineering, 2003, 28(7): 761-781.
[9] J. Yang, X.C. Yin, Z.H. Liu, P.B. Qian. "Sub-plastic impacts of rigid mass on free-free beam." Journal of Nanjing University of Science and Technology´╝î2012, 35(6)´╝Ü837-842.
[10] J. Yang, X.C. Yin, Z.H. Liu, P.B. Qian. "Elastic viscoplastic sub-impacts of free-free beam struck by rigid mass." Journal of Mechanical Engineering, 2012, 48(1)´╝Ü72~77.
[11] Z.H. Liu, X.C. Yin. "Multiple elastic-plastic impacts between free-free beam and simply supported beam." Journal of Mechanical Engineering, 2010, 46(10): 47-53.
[12] Z.F. Nie, G.T. Yang. "Experimental investigation on large deflection response of a frame impacted by a moving body." Acta Mechanica Solida Sinica, 1991, 12(1): 44-54.
[13] X.C. Yin. "Multiple impacts of two concentric hollow cylinders with zero clearance. International Journal of Solids and Structures," 1997. 34(35-36): 4597-4616.
[14] Z.H. Liu, X.C. Yin. "Multiple elastic-plastic impacts of a simply supported beam struck by a round-nosed mass." Explosion and Shock Waves, 2010, 30(2): 138-144.