炸药爆轰的连续介质本构模型和数值计算方法

A continuum constitutive model and computational method of explosive detonation

假定炸药和爆轰产物处于局部热力学平衡状态,即它们的压力和温度相同,利用热力学基本关系建立炸药爆轰过程的连续介质本构模型的一般理论框架.在此框架下,炸药爆轰本构模型由一组常微分方程构成,包括炸药和爆轰产物的状态方程、简单混合法则、化学反应速率方程和能量守恒方程,易于由成熟的计算方法如梯形法等进行求解.一组广义Maxwell型非线性固体本构形式的微分方程描述了压力和温度随时间的演化速率与应变率和化学反应速率的关系,借助简单混合物理论,其中的系数由炸药和爆轰产物的材料参数确定.未反应的炸药和爆轰产物采用JWL状态方程,化学反应率方程采用Lee-Tarver点火-燃烧二项式模型,模拟PBX-9404炸药的一维冲击波起爆过程和爆轰波传播过程.计算结果表明了本文给出的本构模型和相应计算方法的有效性.

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.