Material behavior: Texture and anisotropy

Abstract

This contribution is an attempt to present a self-contained and comprehensive survey of the mathematics and physics of the material behavior of rocks in terms of texture and anisotropy. Being generally multiphase and polycrystalline, where each single crystallite is anisotropic with respect to its physical properties, texture, i.e., the statistical and spatial distribution of crystallographic orientations, becomes a constitutive characteristic and determines material behavior except for grain boundary effects, i.e., in first-order approximation. This chapter is in particular an account of modern mathematical texture analysis explicitly clarifying terms, providing definitions and justifying their application, and emphasizing its major insights. Thus, mathematical texture analysis is brought back to the realm of spherical Radon and Fourier transforms, spherical approximation, and spherical probability, i.e., to the mathematics of spherical tomography.