Studies in the theory of shock propagation in solids

Abstract

In Part I a single-parameter visco-elastic model of a shear-yielding solid is defined for which a permanent-regime solution of the equations of motion exists for any finite compression. The ‘profile’ of this compression as a function of distance is obtained in the form of an integral which can be evaluated when the velocity of propagation is known as a function of final compression. It is assumed that the permanent-regime solution approximates actual shock waves, and that the velocity of the permanent-regime profile equals the shock velocity. Observed shock speeds are used to compute shock profiles in a number of metals. The maximum slope of the profile for any one metal increases with increasing compression. The limiting value of the maximum slope as the volume is extrapolated to zero gives a numerical estimate of the viscosity parameter, and this has been done for Al, Pb, Sn, Zn, and Zr. In Part II Zener's linear theory of anelasticity has been generalized to materials with cubic crystal structure. The theory of the propagation and attenuation of plane waves, both longitudinal and transverse, along a principal axis of the crystal is presented. The combined effects of relaxation mechanisms and thermal diffusion are included. The significance of the results for the theory of shock propagation are discussed and several questions are raised for later discussion. In Part III the general equations for propagation of steady-state compression profiles in shear-yielding, heat-conducting, anelastic solids are given. Methods of solution by successive approximation are developed for Hookean solids, with both adiabatic and isothermal (very steep) profiles, and for non-Hookean solids with shock profiles. The results of Part I are corrected to include the effects of thermal conductivity and anelasticity. Heating aftereffects of shocks are discussed, including the effects of irreversible heating due to viscous yielding, etc., and it is shown how the temperature of the solid after passage of a shock profile may be calculated.