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Some basic thermodynamic relationships are used to develop a theroretical framework for modeling the detonation in explosives, on the assumption that explosive and detonation product are in a local thermodynamic equilibrium state, i.e., their pressures and temperatures are identical. Using this framework, a continuum constitutive model for explosive detonation is composed of a group of ordinary differential equations including the state equations of explosive and its product, simple mixing law, reaction rate equation and energy conservation equation, which are easily solved by a mature computational method such as trapezoidal rule. A group of nonlinear constitutive equations in a generalized Maxwellian form describe the relationship among the time evolution rates of pressure and temperature, the strain rate, and the chemical reaction rate. Coefficients appearing in the constitutive equations are determined only by parameters of the explosive and the product through using simple mixing rule. The continuum constitutive model and the corresponding computational method are verified by simulating the detonation behaviour of PBX9404 impacted by high velocity Cu flyer, and in the simulation the JWL equation of state for unreacted explosive and detonation product and the two-term Lee-Tarver reaction rate equation are adopted.
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Keywords:
- explosive detonation /
- constitutive equation /
- reaction rate /
- numerical simulation
[1] Sun J S, Zhu J S 1995 Theory of Detonation Physics (Beijing: National Denfense Industry Press) (in Chinese) [孙锦山, 朱建士 1995 理论爆轰物理 (北京: 国工业出版社)]
[2] Sun C W, Wei Y Z, Zhou Z K 2000 Application of Detonation (Beijing: National Denfense Industry Press) (in Chinese) [孙承纬, 卫玉章, 周之奎 2000 应用爆轰物理 (北京: 国工业出版社)]
[3] Mader C L 2008 Numerical Modeling of Explosives and Propellants (New York: CRC Press) p373
[4] Johnson J N, Tang P K, Forest C A 1985 J. Appl. Phys. 57 4323
[5] Sun C W 1986 Chin. J. Comput. Phys. 3 142 (in Chinese) [孙承纬 1986 计算物理 3 142]
[6] Zhang G R, Chen D N 1991 Detonation Dynamics of Agglomerate Detonation (Beijing: National Denfense Industry Press) p142 (in Chinese) [章冠人, 陈大年 1991 凝聚炸药起爆动力学 (北京: 国防工业出版社) 第142页]
[7] Brenan K E, Campbell S L, Petzold L R 1996 Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (Philadelphia: SIAM) p4
[8] Ascher Uri M, Petzold L R 1998 Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (Philadelphia: SIAM)
[9] Hayes D B 1975 J. Appl. Phys. 46 3438
[10] Johnson J N 1981 J. Appl. Phys. 52 2812
[11] Sun H Q, Zhang W H 2006 Chin. J. Energ. Mater. 14 16 (in Chinese) [孙海权, 张文宏2006 含能材料 14 16]
[12] Lee E L, Tarver C M 1980 Phys. Fluids 23 2362
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[1] Sun J S, Zhu J S 1995 Theory of Detonation Physics (Beijing: National Denfense Industry Press) (in Chinese) [孙锦山, 朱建士 1995 理论爆轰物理 (北京: 国工业出版社)]
[2] Sun C W, Wei Y Z, Zhou Z K 2000 Application of Detonation (Beijing: National Denfense Industry Press) (in Chinese) [孙承纬, 卫玉章, 周之奎 2000 应用爆轰物理 (北京: 国工业出版社)]
[3] Mader C L 2008 Numerical Modeling of Explosives and Propellants (New York: CRC Press) p373
[4] Johnson J N, Tang P K, Forest C A 1985 J. Appl. Phys. 57 4323
[5] Sun C W 1986 Chin. J. Comput. Phys. 3 142 (in Chinese) [孙承纬 1986 计算物理 3 142]
[6] Zhang G R, Chen D N 1991 Detonation Dynamics of Agglomerate Detonation (Beijing: National Denfense Industry Press) p142 (in Chinese) [章冠人, 陈大年 1991 凝聚炸药起爆动力学 (北京: 国防工业出版社) 第142页]
[7] Brenan K E, Campbell S L, Petzold L R 1996 Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (Philadelphia: SIAM) p4
[8] Ascher Uri M, Petzold L R 1998 Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (Philadelphia: SIAM)
[9] Hayes D B 1975 J. Appl. Phys. 46 3438
[10] Johnson J N 1981 J. Appl. Phys. 52 2812
[11] Sun H Q, Zhang W H 2006 Chin. J. Energ. Mater. 14 16 (in Chinese) [孙海权, 张文宏2006 含能材料 14 16]
[12] Lee E L, Tarver C M 1980 Phys. Fluids 23 2362
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