Multi-scale modelling and simulation of effective properties of perforated sheets with periodic patterns

The elastic properties of a perforated sheet having hexagonal periodic patterns are evaluated using a representative volume element (RVE). The finite element method (FEM) is employed to evaluate the response of the RVE under periodic boundary conditions and numerical homogenisation technique is applied using the FEM solution to estimate the effective properties of the perforated sheet. Numerical homogenisation results are compared to analytical solutions from literature and experimental results. The RVE used in this work considers the radius formed between attached edges and investigates the effect of radius on the overall properties, which has not been sufficiently investigated in literature. Furthermore, the influence of enforcing periodic boundary conditions on the RVE along the thickness direction for such thin perforated structure is investigated. It is found that the elastic constants are overestimated on enforcing periodicity in the thickness direction.