A representative volume element based on translational symmetries for FE analysis of cracked laminates with two arrays of cracks

A methodology is proposed for the construction of a representative volume element (RVE) for analysis of laminated composites containing two arrays of ply cracks running in different directions. The only requirement is that the cracks in any ply are uniformly spaced, and if more than one ply of a given orientation is cracked, then the crack spacing of individual plies must only be in exact multiples of each other. The spacing of cracks in the two directions can be fully independent. The RVE is constructed through a systematic consideration of translational symmetries present in the cracked laminate. As a result, the boundary conditions on the RVE can be imposed without compromising accuracy. Examples of the application of the RVE methodology are given to illustrate its broad capability and a finite element (FE) stress analysis is performed for these cases to illustrate results such as the crack surface displacements, local stress fields and RVE-averaged elastic properties. For one case, the average properties are compared with experimental results, showing good agreement.