The Effect of Pressure Upon the Elastic Parameters of Isotropic Solids, According to Murnaghan's Theory of Finite Strain

Abstract

Murnaghan's theory of finite deformations is applied to a discussion of the effect of hydrostatic pressure upon the elastic coefficients of an isotropic body, for small strains superposed on the hydrostatic strain. Stress-strain equations for the small strains, and the equations of small motion, are shown to have the same form as those of the classical theory, with elastic parameters which depend upon the pressure. Using a form of elastic potential identical with that of the classical theory, explicit results are found for the pressure coefficients of compressibility, Young's modulus, rigidity and so on; these are compared with such experimental results as are available, with good agreement. A single-constant formula is derived which gives the volume change of such compressible materials as sodium and cesium up to the highest experimental pressure, 45,000 kg/cm2, within the experimental error.