Material Behavior: Texture and Anisotropy

Ralf Hielscher, David Mainprice and Helmut Schaeben
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Ralf Hielscher: Technical University Chemnitz, Applied Functional Analysis
David Mainprice: Technical University Chemnitz, Applied Functional Analysis
Helmut Schaeben: Technical University Chemnitz, Applied Functional Analysis

Chapter 33 in Handbook of Geomathematics, 2010, pp 973-1003 from Springer

Abstract: Abstract This 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 the mathematics of spherical tomography.

Keywords: Texture Analysis; Pole Figure; Harmonic Coefficient; Electron Back Scatter Diffraction; Dirichlet Kernel (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-01546-5_33

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