含空腔高熔点炸药在冲击波作用下的广义插值物质点法
Generalized Interpolation Material Point Approach to High Melting Explosive with Cavities Under Shock
摘要：
接触判据是广义插值物质点法的关键。我们提出了一个改进的标准，通过增加一个开关函数。用该方法研究了含空穴的高熔点炸药在冲击波作用下的动力学响应。本文采用的物理模型是一个弹塑性热力学模型，采用Mie-Grüneissen状态方程。主要研究了冲击速度$v$、空腔尺寸$R$等参数对材料动力学和力学行为的影响。对于两个物体的碰撞，每个物体都有一个空腔，观察到二次碰撞。相应地，两个物体的分离距离$D$在初始碰撞和第二次碰撞之间具有最大值$D_{\max}$。当初始碰撞速度$v$不够大时，空泡以近似对称的方式坍缩，最大分离距离$D_{\max}$随初始碰撞速度$v$的增大而增大。当初始冲击波足够强，使空腔沿冲击波方向非对称坍缩时，$D_{\max}$随$v$的变化不呈现单调行为。我们的数值结果清楚地表明，炸药中空腔的存在有助于产生“热点”。
英文摘要：
Criterion for contacting is critically important for the Generalized Interpolation Material Point(GIMP) method. We present an improved criterion by adding a switching function. With the method dynamical response of high melting explosive(HMX) with cavities under shock is investigated. The physical model used in the present work is an elastic-to-plastic and thermal-dynamical model with Mie-Grüneissen equation of state. We mainly concern the influence of various parameters, including the impacting velocity $v$, cavity size $R$, etc, to the dynamical and thermodynamical behaviors of the material. For the colliding of two bodies with a cavity in each, a secondary impacting is observed. Correspondingly, the separation distance $D$ of the two bodies has a maximum value $D_{\max}$ in between the initial and second impacts. When the initial impacting velocity $v$ is not large enough, the cavity collapses in a nearly symmetric fashion, the maximum separation distance $D_{\max}$ increases with $v$. When the initial shock wave is strong enough to collapse the cavity asymmetrically along the shock direction, the variation of $D_{\max}$ with $v$ does not show monotonic behavior. Our numerical results show clear indication that the existence of cavities in explosive helps the creation of ``hot spots''.
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