Some Problems of Nonlinear Stress Waves in Solids

摘要

The paper considers some fundamental aspects of dynamic loading as produced in a solid by contact explosion or ballistic impact. At such high stress and strain rates, a quasi-static constitutive relation may be used in the formulation of the nonlinear wave equation for the solid with both rigidity and compressibility taken into account. The formalism of the hyperbolic-type wave equation can serve to disclose several fundamental properties of nonlinear stress waves in solids. It is of interest to note that both elastic shock waves and plastic shock waves can exist in tension as well as in compression. For very strong compression the effect of material strength may be neglected, and only plastic shocks become identical with hydrodynamic shocks. Four nonlinear solids are examined in connection with plane waves based on Lagrangian coordinates, and a compact wave equation is presented to cover several simple geometries. (Author)