Three-dimensional stress analysis of textile composites: Part I. Numerical analysis

Three-dimensional stress analysis in a unit-cell of a plain-woven composite was performed by using B-spline displacement approximation. The spline approximation provides continuity of displacement and stress components within each yarn and matrix subregion. Two types of unit-cell problems with and without inter-yarn delamination were considered. A penalty function approach along with a contact surface characteristic function was used to obtain a full-field numerical solution for the frictionless contact problem between delaminated yarn surfaces. Yarn interfaces at yarn-crossover locations represent three-material wedge-type regions resulting in singular stress behavior. In the case of unit-cells with perfect bonding between the yarn interfaces, the numerical values of the inter-yarn normal stress did not exhibit trends typical for unbounded stress behavior, whereas the inter-yarn shear stress components displayed discontinuous behavior typical for numerical results in the vicinity of the stress singularity. In the presence of the delamination, both the inter-yarn normal and shear stress components exhibited unbounded behavior near the singularity. Notably, the inter-yarn normal stress showed signs of singular behavior in both cases of open and closed delaminations. Due to the stress singularity that exists at yarn-crossover locations containing three materials (yarn–yarn–matrix) interface intersections, the full-field numerical solution, even with high-order approximation functions, was not able to capture the directional nonuniqueness of the stress values in the vicinity of the singularity, and therefore calls for incorporation of the asymptotic singular stress analysis, which will be given in a follow-on paper [Sihn and Roy, International Journal of Solids and Structures (accepted for publication)].