Material behaviour – Texture and anisotropy.

International audienceThis contribution is an attempt to present a self-contained and comprehensive survey of the mathematics and physics of material behavior of rocks in terms of texture and anisotropy. Being generally multi-phase and poly-crystalline, 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 the 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, spherical probability, i.e., to themathematics of spherical tomograph