A Computational Library for Determining the Mechanical Properties of Crystals and Polycrystalline Aggregates

Computer modeling of the basic equations of solid mechanics is simplified with a well designed computational library. The weighted arithmetic average and weighted harmonic average are abstract forms of the more concrete upper and lower bounds for the effective elastic moduli of fluid mixtures and solid composites. More rigorous upper and lower bounds for the effective isotropic elastic coefficients of an anisotropic crystal are calculated from the two linear fourth rank tensor invariants. Rock physics transform functions for isotropic homogeneous materials can be used to calculate the compressional wave velocity and shear wave velocity from the mean value of the upper and lower bounds yielding a spherical surface in the three dimensional phase velocity space. The behavior of the velocity surface for a given anisotropic tensor, however, is not easily recognized in the analytical form of the Green-Christoffel equation. The phase-velocity surface for a single crystal deviates from the isotropic velocity due to the inherent nature of the crystal being anisotropic. The amount of deviation and curvature of the surface depends on the symmetry and the values of the stiffness tensor. A generic library of data structures and algorithms makes visualizing and interpreting these results simpler.