Theory and Simulation of Shock Wave Phenomena in Solids and Their Applications to Engineering

采用解析和数值相结合的方法，从微观和宏观两个角度研究了固体中冲击波的力学和热学性质。文中还探讨了它们在工程问题中的可能应用。新的结果如下(1)-(8)：1.基于包含热振动和有限变形的新的热弹性模型对波传播现象进行了分析研究：(1)固体中线性波传播现象的统计热力学。熔点附近现象的奇异性质。(2)考虑微观热振动的固体新连续介质模型分析加速波。冲击波的形成。(3)有限温度至熔点的固体中的弱冲击波。Rankine-Hugoniot关系及其在熔点以下的温度依赖关系。(4)一维晶体固体中的双曲性、凸性和激波。新的热弹性模型的数学结构。(5)固体中激波与加速波相互作用的综合研究。新的连续介质模型中非线性动力学的基本过程。(6)有限温度至熔点的弹性波在固体中的反射和折射。有限温度下固体中冲击波现象的分子动力学模拟：(7)致密硬球系统中的冲击波现象。激波引起的动态相变。(8)黎曼问题：二维晶体固体中的激波、稀疏波和接触波。

Mechanical and thermal properties of shock waves in solids were studied from both microscopic and macroscopic viewpoints by using analytical and numerical methods. Their possible applications to engineering problems were also investigated. New results explained in the following (1)-(8) have been obtained:1.Analytical study of wave propagation phenomena based on the new thermo-elastic model incorporating thermal vibration and finite deformation:(1) Statistical-thermodynamics of linear wave propagation phenomena in solids. Singular properties of the phenomena near the melting points.(2)Acceleration waves analyzed by the new continuum model of solids incorporating microscopic thermal vibration. Formation of shock waves.(3)Weak shock waves in solids at finite temperatures up to the melting point. Rankine-Hugoniot relations and their temperature dependences up to the melting point.(4)Hyperbolicity, convexity and shock waves in one-dimensional crystalline solids. Mathematical structure of the new thermo-elastic model.(5) Comprehensive study of interaction between a shock wave and an acceleration wave in solids. Fundamental process in the nonlinear dynamics of the new continuum model.(6) Reflection and refraction of elastic waves in solid at finite temperatures up to the melting point.2. Molecular dynamics simulations on shock wave phenomena in solids at finite temperatures:(7) Shock wave phenomena in a dense hard-sphere system. Dynamic phase transition induced by a shock wave.(8)The Riemann problem: Shock, rarefaction and contact waves in a 2-dimensional crystalline solid.