Discussion of "Woven fabric composite material model with material non-linearity for non-linear finite element simulation" by Tabiei and Jiang - [Int. J. Solids Struct. 36 (1999) 2757-2771]

Tabiei and Jiang (1999) present an approach in which, through homogenization, a model for a woven composite material is developed. The model is suitable for implementation in commercial finite element (FE) packages (to represent a material point). This then enables analysis of structures composed of the woven composite while providing the local stresses and strains in the woven composite yams at the FE material points. Hence, the objective of the paper, in my opinion, is extremely worthwhile. This type of multi-scale approach to structural analysis shows potential for improving designs, as well as streamlining the design procedure, for structures composed of advanced materials (such as woven composites). In developing the model for the woven composite, Tabiei and Jiang (1999) identify a repeating unit cell (in the plane of the weave) and divide the unit cell into subcells. Each subcell is then homogenized through the weave's thickness via iso-stress and iso-strain conditions. The composite is thus represented, at this point, by a repeating unit cell consisting of an array of two-dimensional subcells, each with effective (homogenized) properties (see Fig. 1). The next step in the model development involves homogenization of the two-dimensional subcells to obtain the effective constitutive equations for the repeating unit cell (Tabiei and Jiang, 1999, Section 2.2, p. 2764). Here, the authors state, "... it is assumed that the average in-plane strains and stresses among subcells have the following relationships..." (Tabiei and Jiang, 1999, p. 2764), and 16 equations are presented, which relate the local (subcell) and global (homogenized) stresses and strains in the repeating unit cell. Although no reference is given, it is my opinion that these equations are, in actuality, the generalized method of cells (GMC) equations developed by Paley and Aboudi (1992). Figs. I and 2 compare the geometry employed by Tabici and Jiang with that of GMC, while Table I presents the correspondence between the equations presented by Tabiei and Jiang (1999) and the GMC equations presented by Paley and Aboudi (1992).