Unit cell modelling of textile laminates with arbitrary inter-ply shifts

Abstract Deformation and failure mechanisms of textile laminates are strongly affected by mutual shift of the plies. To model arbitrarily stacked laminate within a traditional framework of multi-scale modelling, one must construct a representative volume element (RVE), which includes all the plies. This is a time consuming and computationally expensive work. As an alternative, the paper suggests a technique that allows setting problems on one unit cell of a single ply, i.e. a volume smaller than RVE of the laminate. The technique approximates the stress field in a ply by combination of stress fields obtained in two additional problems. Boundary conditions (BC) in these problems imitate the interaction of the unit cell with surrounding media. Once these problems are solved, the solution for arbitrary number of plies is composed analytically. The proposed technique respects inter-ply configurations, accounts for the number of plies, distinguishes the ply position, and reproduces the meso stress state with a good accuracy. The technique is validated against reference solutions obtained for the entire laminate.