Z-M. Huang/Computers and Structures 80(2002)1159-1176 Textile lamina 45 through a rotation by 45.(see, Ref. [8]), only the analysis for a diamond braid lamina is elaborated in this section. Furthermore. no thermal residual stress is as- sumed to occur in the lamina (this is the case when th Unit cel amina is fabricated at room temperature as in a sub sequent example). RVE a schematic diagram to show the sub-division of a braided fabric lamina is indicated in Fig. 7.a diamond structure is shown in Fig. 8, which is fabricated from UD composites two yarns(called fill and warp yarns respectively) in terracing one after another (Fig. 7(a)). The braiding Fig. 6. Analysis procedure for a textile fabric reinforced lam- angle, 0, is defined as an inclined angle between the yarn axis and the fabric longitudinal direction(Figs. 8 and 7(b)). As the fabric structure can be constructed by re- peating some unit cell(Fig. 7(b)), the analysis for the and an assemblage. The textile lamina is first sub- braid lamina can be achieved by that for a unit cell as divided into a number of UD composites, to which the long as all the unit cells in the composite are under the bridging model can be applied. Then all the UD cor same load/deformation condition. However, the unit cell posites are assembled together to obtain the three basic shown in Fig. 7(b) can be further divided into four sub quantities of the original textile lamina, i.e., the internal cells that are identical or symmetrical. Thus, we only stress increments in the fiber and matrix materials and need to analyze one sub-cell, which is called a rvE for the lamina instantaneous compliance matrix. the braid lamina The most customised work in the analysis of a textile The Rve is first sub-divided in the fabric plane into composite is to identify the unit cell or the rve geo- sub-elements [8], as shown in Fig. 7(c). Suppose that the metry of the textile structure under consideration. This total number of the sub-elements is M. Each sub-ele- identification is necessary for the sub-division as well as ment, Fig. 7(d), can have at most four material layers, for the assemblage. In this paper, only the simplest i.e., the braider yarn l, the braider yarn 2, and the top extile structures are taken into account, for easy illus- and bottom pure matrix layers. These material layers are ration purpose. For woven and braided fabrics, the. considered as UD composites in their respective local simplest structures are a plain weave and a diamond coordinate systems(both the pure matrix layers can be braid [21]. As the plain weave can be obtained geomet regarded as a UD composite with a zero fiber volume Single layer lat L, y, local system Subdivision of a suh-ele Yarn 2 Fig. 7. A schematic diagram to show analysis procedure for a braided fabric lamina.and an assemblage. The textile lamina is first sub￾divided into a number of UD composites, to which the bridging model can be applied. Then all the UD com￾posites are assembled together to obtain the three basic quantities of the original textile lamina, i.e., the internal stress increments in the fiber and matrix materials and the lamina instantaneous compliance matrix. The most customised work in the analysis of a textile composite is to identify the unit cell or the RVE geo￾metry of the textile structure under consideration. This identification is necessary for the sub-division as well as for the assemblage. In this paper, only the simplest textile structures are taken into account, for easy illus￾tration purpose. For woven and braided fabrics, the simplest structures are a plain weave and a diamond braid [21]. As the plain weave can be obtained geomet￾rically from a diamond braid with a braiding angle of 45 through a rotation by 45 (see, Ref. [8]), only the analysis for a diamond braid lamina is elaborated in this section. Furthermore, no thermal residual stress is as￾sumed to occur in the lamina (this is the case when the lamina is fabricated at room temperature as in a sub￾sequent example). 7.1. Sub-division A schematic diagram to show the sub-division of a braided fabric lamina is indicated in Fig. 7. A diamond structure is shown in Fig. 8, which is fabricated from two yarns (called fill and warp yarns respectively) in￾terlacing one after another (Fig. 7(a)). The braiding angle, h, is defined as an inclined angle between the yarn axis and the fabric longitudinal direction (Figs. 8 and 7(b)). As the fabric structure can be constructed by re￾peating some unit cell (Fig. 7(b)), the analysis for the braid lamina can be achieved by that for a unit cell as long as all the unit cells in the composite are under the same load/deformation condition. However, the unit cell shown in Fig. 7(b) can be further divided into four sub￾cells that are identical or symmetrical. Thus, we only need to analyze one sub-cell, which is called a RVE for the braid lamina. The RVE is first sub-divided in the fabric plane into sub-elements [8], as shown in Fig. 7(c). Suppose that the total number of the sub-elements is M. Each sub-ele￾ment, Fig. 7(d), can have at most four material layers, i.e., the braider yarn 1, the braider yarn 2, and the top and bottom pure matrix layers. These material layers are considered as UD composites in their respective local coordinate systems (both the pure matrix layers can be regarded as a UD composite with a zero fiber volume Fig. 6. Analysis procedure for a textile fabric reinforced lam￾ina. Fig. 7. A schematic diagram to show analysis procedure for a braided fabric lamina. Z.-M. Huang / Computers andStructures 80 (2002) 1159–1176 1167