Phantom-Element Technique for Periodic Deformation Analysis of Plain Fabrics Using LS-DYNA

Unit-cell modelling is one of the useful methods to analyze deformation in periodic structures like honeycombs, perforated boards, and woven fabrics. The initial state of the structures is considered to be stress-free in ordinal deformation analysis, but in actual practice, the analysis is difficult, because initial stresses like assembly stress and residual stress need to be considered, as they are known to affect the results. In this study, a technique of taking into account the initial-stress state in woven fabrics is discussed, which has resulted in the establishment of a precise design method for textiles. LS-DYNA, which is a general-purpose finite element (FE) software, has been utilized to simulate the complex deformations in woven fabrics. In this software, a function of the global constraint on boundary conditions facilitates the analysis of periodic structures, but causes difficulties in computing the initial stress states in woven fabrics, as the conditions of mechanical equilibrium have to be satisfied in the governing equations. In particular, duplicated definitions of forced displacement and periodic deformation make the computation impossible, hence, a phantom-element has been introduced to ease the FE analysis by defining these quantities. A unit-cell of the woven fabric is identified and the initial states in stressed conditions can be estimated for periodic structures of plain-woven fabrics by a periodic-analysis technique of LS-DYNA coupled with the phantom-element, which yields a weaving motion of the yarn in plain-woven fabrics.