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

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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.