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拉格朗日分析方法是通过测量各个拉格朗日位置处的物理量历程 来分析材料内部该位置处的其他物理量的变化, 进而认识材料的动态力学性能.但现有的拉格朗日分析方法在已知粒子速度情况下, 求解方法仍有不足.针对这一情况, 提出了沿时间逐步求解方法, 该方法能够在不做任何假定的情况下求解出应力, 从而从根本上解决了只测量粒子速度这一物理量时求解应力的困难. 并利用该方法对一组混凝土在冲击作用下的实验数据进行了处理, 计算得到了相应的应变波形、应力波形以及加、卸载全过程的应力-应变曲线, 进而揭示出混凝土材料与应变率相关的弹-塑性本构关系的特征.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 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 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 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 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 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 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 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 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 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 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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