Variety of fiber orientation tensors

Fiber orientation tensors are established descriptors of fiber states in (thermo-)mechanical material models for fiber-reinforced composites. In this paper, the variety fourth-order is analyzed and specified by parameterizations admissible parameter ranges. The combination ranges allows studies on mechanical response different architectures. Linear invariant decomposition with focus index symmetry leads to a novel compact hierarchical parameterization, which highlights central role isotropic state. Deviation from state given triclinic harmonic tensor simplified structure coordinate system, spanned second-order tensor. Material symmetries reduce number independent parameters. requirement positive-semi-definiteness defines Admissible transversely planar cases closed form orthotropic visualized discussed detail. Sets discrete unit vectors, leading selected states, given.