3D Braided Geometry Structures Based on Space Group

Abstract

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.

Investigation of the classification and properties of three-dimensional textile fabrics

“…As shown in Figure 4 to the global coordinate system. 36 The stiffness matrix [ ] C′ in the global coordinate system can be deduced by formula (9)…”

“…3 By describing the textile fabrics with point group and space group, the geometric structures of fabrics could be derived and classified reasonably and effectively, so that the types of the textile preform were no longer limited to process distinction. [8][9][10] The advanced 3D spacer composites were classified based on the different factors depending on the orientation of the yarn, the yarn sets, and the geometry. 11 Based on the aforementioned classification method, the meso-structure and mechanical properties of 3D textile fabrics have been extensively studied in recent decades.…”

3D Braided Material Based on Space Group <i>R</i>3 Symmetry

“…Thus there is an urgent need to develop a more three-dimensional processing. The new three-dimensional woven prediction research is still in its infancy [12].…”

“…With reference to the research methods of symmetry group, researches on unit cell geometry of braided materials can be summarized. According to the space group and the space group, symmetry operations can be deduced from a large number of new three-dimensional yarn crossover methods [12]. A new geometry structure of 3D braided material was deduced by using space point S6 corresponding to symmetry operations and the symmetry of space group P3, and author researched its processing and properties [14].…”

Meso-structure and processing of three-dimensional braided material based on space group P4 symmetry

“…A series of new 3D braided geometries was deduced. 10–18 According to the symmetry of space group P3true¯, a 3D braided geometry was obtained using translation and symmetry operations of the unit. 11,12 The 3D tubular braided composites based on the space group P3true¯ symmetry were studied, and the feasibility of the 3D braided process was verified by the literature.…”