Three-dimensional stress distributions in hexagonal aeolotropic crystals

Abstract

The conditions for equilibrium in an elastically stressed hexagonal aeolotropic medium (transversely isotropic) are formulated, and solutions are found in terms of two ‘harmonic’ functions ø 1 , ø 2 , which are solutions of ν 1 , ν 2 being the roots of a certain quadratic equation. It is also shown that in the case of axially symmetrical stress systems the solution may be expressed in terms of the third-order differential coefficients of a single stress function Φ. The solutions for an isotropic medium may be deduced as a special case. The problems of nuclei of strain in such a hexagonal solid are solved, and the results for zinc and magnesium contrasted with those for an isotropic solid.