Models for shear properties/behavior of dry fibrous materials at various scales: a review

During forming operations of dry fibrous materials in order to get the composite preforms, the deformation mode is substantially determined by the occurring shear strains. Consideration of the material shear response namely from the theoretical point of view has gained high importance because multi-scale nature and anisotropy of fibrous materials complicates their experimental investigation, which raises the question of the tests realizability, complexity, and cost. This work analyses and classifies the existing theoretical approaches for the shear prediction with respect to the mathematical principles employed, as well as with respect to the architecture of diverse fibrous materials, to which the approach can be applied. Both classifications depend in turn on the main criterion of classification emphasized here - the scale of observation of the shear load. According to the theoretical framework, the approaches form the main groups based either on purely geometrical reasoning, or on finite elements analysis, or on energy minimization, or on forces equilibrium principle. The approaches are compared according to the total of mechanical factors included in their analysis and typical for a certain stage of shear load and a certain scale (micro-, meso-, or macro-). The advantages and difficulties of each of the methods are evaluated.