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

Abstract

A unit cell geometrical structure was found with the use of symmetry operations corresponding to the point group C3. Based on the symmetry of space group R3, a 3D braided geometrical structure was obtained by transforming the unit-cell. The features corresponding to this braided structure were studied. The fiber volume percentage and variational tendencies of the material were predicted by establishing a geometric model.

Meso-structure and modeling of a new three-dimensional braided tubular material

“…It is determined by the yarn linear density Γ( Texy/1000) and the density of fiber material ρ( g/cm3). 27…”

“…It is determined by the yarn linear density C(Texy=1000) and the density of fiber material q(g=cm 3 ). 27 The reduction coefficient k is introduced to simplify the calculation.…”

Processing technique and geometric model of an imperfect orthogonal 3D braided material

“…where The font R represents the equivalent radius of the yarn. It is determined by the yarn linear density À ¼ Texy=1000 ð Þ and the density of fiber material g=cm 3 À Á [21]. The symbol A is the cross-sectional area of the yarn in natural state.…”

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.…”

“…15,16 The feasibility of a new type of 3D braided geometry based on the space group R 3 symmetry was proposed, and an experiment verified the feasibility of the 3D braided process. 17,18…”