Multi-stage analysis of the tensile rigidity of plain-weave structures using a homogenization method considering internal stresses

In plain-weave structures, such as plain-weave fabrics and thread meshes, the characteristic distribution of internal stress development varies due to tensile and bending deformations during the weaving process. This internal stress can be considered an important factor with respect to the tensile rigidity of the final product. This paper presents a computational method for simulating the weaving process and evaluating the stress distribution within a woven structure for an experiment-free evaluation of product rigidity. The plain-weave structure is analyzed using the finite element method, and its tensile rigidity is assessed through a homogenization approach employing periodic unit cells. Specifically, multi-stage diagrams of the plain-weave tensile simulation are discussed in this paper. The weaving stage controls the motions that occur during the weaving process. To assess the effect of the internal stress distribution, we compare three cases: a case with weaving-induced residual stresses and strains removed, a case with all residuals retained, and a case that evaluates the contraction of the fabric after release from the loom constraints. The results show that the case with residuals removed underestimates the tensile rigidity, whereas the case with residuals exhibits a significantly higher level of rigidity. The tensile response of the loom-release case falls between those of the two cases. The results indicate that the increased rigidity results from the contact stresses above the interlacing point of the threads. This paper reveals the importance of internal stress in plain-weave structures using appropriate unit cells for different stages.