Orientation distribution function in non-affine rotations

摘要

The orientation distribution function (ODF) for a class of directional elements, represented by unit vectors or orthonormal triads, which are embedded in a deforming continuum, is obtained by a novel approach in closed analytical form as a function of appropriate deformation and rotation measures, for orientational processes which can be characterized as non-affine rotations. The main conceptual innovation is the introduction of a fictitious motion defined locally in The neighborhood of a material point, such that a directional element which follows non-affine Rotation in relation to the real motion, follows affine rotation in relation to the fictitious motion.