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Lagrangian analysis method is re-analyzed, in which by measuring the physical variables of each Lagrangian positions the other physical variables of these positions of the material is analyzed, and then the dynamic mechanical properties of materials can be determined. However, the existing Lagrangian analysis methods are still inadequate when the particle velocity is known. In this paper, a new Lagrangian analysis method, with only particle velocity known, is developed, which is called step by step method along the time. The method does not make any assumption, and it can solve the problem when only particle velocity wave profiles are measured. A set of experimental data of concrete under impact is processed with the method, and the corresponding strain wave, stress wave, and stress-strain relations of the whole process of loading and unloading are calculated. Thus the strain rate dependent elastic-elastic constitutive characteristics of the concrete are revealed.
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Keywords:
- Lagrangian analysis /
- constitutive relation /
- stress-strain /
- concrete
[1] Wang Y G, Zhang Y P, Wang L L 2008 Acta Phys. Sin. 57 7789 (in Chinese) [王永刚, 张远平, 王礼立 2008 物理学报 57 7789]
[2] Chen D N, Fan C L, Hu J W, Wu S X, Wang H R, Tan H, Yu Y Y 2009 Acta Phys. Sin. 58 2612 (in Chinese) [陈大年, 范春雷, 胡金伟, 吴善幸, 王焕然, 谭华, 俞宇颖 2009 物理学报 58 2612]
[3] Peng J X, Jing F Q, Wang L L, Li D H 2005 Acta Phys. Sin. 54 2194 (in Chinese) [彭建祥, 经福谦, 王礼立, 李大红 2005 物理学报 54 2194]
[4] Hu J B, Yu Y Y, Dai C D, Tan H 2005 Acta Phys. Sin. 54 5750 (in Chinese) [胡建波, 俞宇颖, 戴诚达, 谭华 2005 物理学报 54 5750]
[5] Sun C W, Wei Y Z, Zhou Z K 2000 The Applied Detonation Physics (Vol. 1) (Beijing: National Defence Industry Press) p348 (in Chinese) [孙承纬, 卫玉章, 周之奎 2000 应用爆轰物理(第一版) (北京:国防工业出版社) 第348页]
[6] Fowles R, Williams R F 1970 J. Appl. Phys. 41 360
[7] Fowles R 1970 J. Appl. Phys. 41 2740
[8] Cowperthwaite M, Williams R F 1971 J. Appl. Phys. 42 456
[9] Grady D E 1973 Geo. Res. 78 1299
[10] Seaman L 1974 J. Appl. Phys. 45 4303
[11] Li X L 1985 Explosion and Shock Waves 5 46 (in Chinese) [李孝兰 1985 爆炸与冲击 5 46]
[12] Cai H Y, Tang Z P 1990 J. China Univ. Sci. Technol. 20 48 (in Chinese) [柴华友, 唐志平 1990 中国科学技术大学学报 20 48]
[13] Cai H Y, Tang Z P 1992 Explosion and Shock Waves 12 259 (in Chinese) [柴华友, 唐志平 1992 爆炸与冲击 12 259]
[14] Gupta Y M 1984 Polym. Eng. Sci. 24 851
[15] Forest C A, Wackerle J, Dick J J 1989 Proc. of 9th Int. Symp. on Detonation Portland, USA, August 28-September 1, 1989 p683
[16] Wang L L, Zhu J, Lai H W 2010 Chinese Journal of High Pressure Physics 24 279 (in Chinese) [王礼立, 朱珏, 赖华伟 2010 高压物理学报 24 279]
[17] Wang L L, Zhu J, Lai H 2011 Strain 47 173
[18] Fowles R 1973 Dynamic Response of Materials to Intense Impulsive Loading (1st Ed.) (Ohio: Wright Patterson Air Force Base, Air Force Materials Laboratory) p416
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[1] Wang Y G, Zhang Y P, Wang L L 2008 Acta Phys. Sin. 57 7789 (in Chinese) [王永刚, 张远平, 王礼立 2008 物理学报 57 7789]
[2] Chen D N, Fan C L, Hu J W, Wu S X, Wang H R, Tan H, Yu Y Y 2009 Acta Phys. Sin. 58 2612 (in Chinese) [陈大年, 范春雷, 胡金伟, 吴善幸, 王焕然, 谭华, 俞宇颖 2009 物理学报 58 2612]
[3] Peng J X, Jing F Q, Wang L L, Li D H 2005 Acta Phys. Sin. 54 2194 (in Chinese) [彭建祥, 经福谦, 王礼立, 李大红 2005 物理学报 54 2194]
[4] Hu J B, Yu Y Y, Dai C D, Tan H 2005 Acta Phys. Sin. 54 5750 (in Chinese) [胡建波, 俞宇颖, 戴诚达, 谭华 2005 物理学报 54 5750]
[5] Sun C W, Wei Y Z, Zhou Z K 2000 The Applied Detonation Physics (Vol. 1) (Beijing: National Defence Industry Press) p348 (in Chinese) [孙承纬, 卫玉章, 周之奎 2000 应用爆轰物理(第一版) (北京:国防工业出版社) 第348页]
[6] Fowles R, Williams R F 1970 J. Appl. Phys. 41 360
[7] Fowles R 1970 J. Appl. Phys. 41 2740
[8] Cowperthwaite M, Williams R F 1971 J. Appl. Phys. 42 456
[9] Grady D E 1973 Geo. Res. 78 1299
[10] Seaman L 1974 J. Appl. Phys. 45 4303
[11] Li X L 1985 Explosion and Shock Waves 5 46 (in Chinese) [李孝兰 1985 爆炸与冲击 5 46]
[12] Cai H Y, Tang Z P 1990 J. China Univ. Sci. Technol. 20 48 (in Chinese) [柴华友, 唐志平 1990 中国科学技术大学学报 20 48]
[13] Cai H Y, Tang Z P 1992 Explosion and Shock Waves 12 259 (in Chinese) [柴华友, 唐志平 1992 爆炸与冲击 12 259]
[14] Gupta Y M 1984 Polym. Eng. Sci. 24 851
[15] Forest C A, Wackerle J, Dick J J 1989 Proc. of 9th Int. Symp. on Detonation Portland, USA, August 28-September 1, 1989 p683
[16] Wang L L, Zhu J, Lai H W 2010 Chinese Journal of High Pressure Physics 24 279 (in Chinese) [王礼立, 朱珏, 赖华伟 2010 高压物理学报 24 279]
[17] Wang L L, Zhu J, Lai H 2011 Strain 47 173
[18] Fowles R 1973 Dynamic Response of Materials to Intense Impulsive Loading (1st Ed.) (Ohio: Wright Patterson Air Force Base, Air Force Materials Laboratory) p416
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