3D braided group theory is dissertated. The analysis procedure is described from the existing braided geometry structure to the braided space group; 3D braided geometrical structures are finally described by means of group theory. Some of novel 3D braided structures are deduced from the braided space groups. By describing the 3D braided materials with braided space point and braided space groups, the braided space groups are not always the same as symmetry groups of crystallographic because novel lattices can be produced and the reflection operation cannot exist in braided space point groups. Braided point and space groups are theoretical basis for deriving the novel braided geometry structure.
A novel geometry structure of unit cell was deduced by using the point group S6 corresponding to symmetry operations. Based on the symmetry of space group P3, a new 3D braided material was obtained by transforming the new unit cell symmetrically. The plate processing corresponding to this geometry structure was studied. The fiber volume percentage and its variation tendency of the 3D braided material were predicted through establishing mathematical model.
The matrix representation of space point group is used in transferring the elastic matrix of the braided yarn based on the symmetries of braided composites representative volume element (RVE) meso-geometrical structure. The off-axis elastic matrixes of the whole braided yarns of the RVE are deduced. With a use of meso-mechanical model based on the mixture rule, the yarn segments off-axis elastic matrixes in the RVE and matrixs one are summed with weight; Equivalent elastic matrix of 3D braided composites was deduced. Equivalent engineering elastic constants are achieved in the end. The model can be applied in 2D braided composites mechanical analysis if its geometry is satisfied to the symmetries corresponding to plain point group.
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