标题： 强圆柱形和球形冲击波在固体材料中的收敛性 显示英文标题

标题： On the Convergence of Strong Cylindrical and Spherical Shock Waves in Solid Materials

摘要： 在本文中，我们提出了基于几何冲击动力学（GSD）理论的冲击压缩固体材料行为的描述。 GSD已被成功应用于各种气体动力学问题，这里我们采用它来研究固体材料中圆柱对称和球面对称收敛冲击波的传播。 在强冲击极限下获得了冲击动力学方程的解析解，假设固体材料是均匀和各向同性的，并遵循Mie-Gruneisen状态方程。 得到了冲击速度、压力、质量密度、粒子速度、温度、声速、绝热体积模量以及强收敛冲击前沿后的熵变的无量纲表达式。 探讨了（i）从收敛轴或中心（r=0）的传播距离r的变化，（ii）Gruneisen参数的变化，以及（iii）材料参数的变化对冲击速度和收敛冲击前沿后区域的影响。 结果表明，当冲击聚焦于轴或原点时，冲击速度、压力、温度和熵变在冲击压缩的钛Ti6Al4V、不锈钢304、铝合金6061-T6等材料中增加。 显示英文摘要

摘要： In this article, we present a description of the behaviour of shock-compressed solid materials following the Geometrical Shock Dynamics (GSD) theory. GSD has been successfully applied to various gas dynamics problems, and here we have employed it to investigate the propagation of cylindrically and spherically symmetric converging shock waves in solid materials. The analytical solution of shock dynamics equations has been obtained in strong-shock limit, assuming the solid material to be homogeneous and isotropic and obeying the Mie-Gruneisen equation of state. The non-dimensional expressions are obtained for the velocity of shock, the pressure, the mass density, the particle velocity, the temperature, the speed of sound, the adiabatic bulk modulus, and the change-in-entropy behind the strong converging shock front. The influences as a result of changes in (i) the propagation distance r from the axis or centre (r=0) of convergence, (ii) the Gruneisen parameter, and (iii) the material parameter are explored on the shock velocity and the domain behind the converging shock front. The results show that as the shock focuses at the axis or origin, the shock velocity, the pressure, the temperature, and the change-in-entropy increase in the shock-compressed titanium Ti6Al4V, stainless steel 304, aluminum 6061-T6, etc.