Analytical and optimization procedures for determination of all elastic constants of anisotropic solids from group velocity data measured in symmetry planes

Abstract

Analytical and optimization methods of determining all elastic constants of elastically anisotropic solids from the group velocities measured in various directions in the symmetry planes are described. The group velocities in various directions of the specimen are measured, using broadband pointlike and line-type sources in combination with pointlike detectors, and changing a source-to-detector orientation. The mixed index elastic constants of the specimen are determined using analytic formulas that relate the elastic constants to the group velocity in an arbitrary direction on the symmetry plane. It is demonstrated that given the numerous group velocity data, one can efficiently determine the elastic constants by first converting them into phase velocity data and then applying the least-squares optimization methods to the phase velocity data. Examples are provided with specimens of transversely isotropic zinc, cubic silicon, and orthotropic fiber-reinforced poly ether ether kethon.