Statistical methods for mechanical characterization of randomly reinforced media

Table 1 Main morphological descriptors and their properties

Function	Order	Measure	Material	Sample dimensions
Indicator function	Lower	Presence of phase	Any random media	2D and 3D
Correlation function	Higher	Spatial correlation	Any random media	2D and 3D
Surface correlation functions	Higher	Interfaces distribution	Any random media	2D and 3D
Pore size distribution function	Lower	Level of porosity	Porous media	Only 3D
Cluster function	Higher	Particles clustering	Any random media	Only 3D
Lineal path function	Lower	Connectedness of microstructure	Any random media	2D and 3D
Chord length distribution function	Lower	Connectedness of microstructure and particles shape	Any random media	2D and 3D
Nearest neighbor functions	Lower	Particles distribution	Particle-reinforced media	2D and 3D
Orientation distribution function	Lower	Grain orientation, macroscopic texture	Polycrystals	Only 3D
Misorientation distribution function	Lower	Orientation of local arrangement of grains	Polycrystals	Only 3D
Micro-texture function	Lower	Amount of clustering of orientations and misorientations	Polycrystals	Only 3D