Abstract
Based on the general conservation laws in continuum mechanics, the Eulerian and Lagrangian descriptions of the jump conditions of shock waves in 3-dimensional solids were presented respectively. The implication of the jump conditions and their relations between each other, particularly the relation between the mass conservation and the displacement continuity, were discussed. Meanwhile the shock wave response curves in 3-dimensional solids, i.e. the Hugoniot curves were analysed, which provide the foundation for studying the coupling effects of shock waves in 3-dimensional solids.
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References
Whitham G B. Linear and Nonlinear Waves[M]. Wiley-interscience Publication, New York, 1973.
Han Zhaoyuan, Yin Xiezhen. Shock Dynamics[M]. Kluwer Academic Publisher/Science Press, Netherland, 1992 (in Chinese).
Lee E H. Plastic-wave propagation analysis and elastic-plastic theory at finite deformation[C]. In: Burke J J, et al (eds). Shock Waves and the Mechanical Properties of Solids. Syracuse University Press, New York, 1971, 210–255.
Jing Fuqian. Introduction of the Experiment Equations of State(second edition)[M]. Science Press, Beijing, 1999 (in Chinese).
Ting T C T, Li Yongchi. Eulerian formulation of transport equations for three-dimensional shock waves in simple elastic solids[J]. Journal of Elasticity, 1983, 13(3): 295–310.
Li Yongchi, Ting T C T. The Lagrangian description of the shock wave transfer equation in 3 dimensional elastic solids[J]. Applied Mathematics and Mechanics (English Edition), 1982, 3(4): 491–506.
Li Yongchi, Ting T C T. Simple waves and shock waves generated by an incident shock wave in two-dimensional hyperalastic materials[J]. Transactions of the ASME, 1984, 51(3): 586–594.
Li Yongchi, Liu Lufeng, Tang Zhijing. Studies on oblique reflection of shock wave in nonlinear elastic media[J]. Explosion and Shock Waves, 1988, 8(1): 7–14 (in Chinese).
Liu Lufeng, Li Yongchi, Tang Zhijing. Studies on oblique reflection of shock wave in nonlinear elastic media(II)[J]. Explosion and Shock Waves, 1989, 9(3): 206–211 (in Chinese).
Tang Zhijing, Ting T C T, Li Yongchi. Two-dimensional stress wave analysis in incompressible elastic solids[J]. Applied Mathematics and Mechanics (English Edition), 1989, 10(8): 701–712.
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Project supported by the National Natural Science Foundation of China (No.10272097) and the Foundation of National Key Laboratory of Ballistics (No.51453040101zk0103)
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Li, Yc., Yao, L., Hu, Xz. et al. Some problems on jump conditions of shock waves in 3-dimensional solids. Appl Math Mech 27, 187–194 (2006). https://doi.org/10.1007/s10483-006-0206-z
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DOI: https://doi.org/10.1007/s10483-006-0206-z