Homogenisation of porous thin films and perforated layers: Comparison of analytical and numerical approaches

• Effective properties of thin films with various pore structure and content are evaluated.
• Results of self-consistent method, Mori–Tanaka approach and numerical experiments are compared.
• Relation between porosity and inter-pore distance for random pore structure is shown.
• Effect of matrix Poisson’s ratio on effective elastic properties is demonstrated.
• Guidelines for the practical application of the above approaches are given.

The mechanical properties of porous thin films and perforated layers are affected by pore content, shape and arrangement. The experimental determination of the in-plane mechanical properties of such materials is challenging, yet reliable data are essential for materials development and component design. Analytical and numerical approaches therefore provide valuable, supplementary tools for evaluating the effect of porosity on the mechanical properties of such materials.The applicability of both the classical self-consistent method and the Mori–Tanaka approach to the estimation of the effective elastic properties of porous thin films and perforated layers is investigated in this paper. For generic model microstructures with various arrangements of pores, variable pore content and varying matrix Poisson’s ratio, the effective elastic properties predicted by the classical self-consistent method and by the Mori–Tanaka approach are quantitatively compared with results obtained by numerical experiments. Based upon this comparison, the range of validity of both the classical self-consistent method and the Mori–Tanaka approach with regard to the different arrangements of pores investigated is defined, and the deviation to be expected if critical values of pore content or inter-pore distance are exceeded and interactions between adjacent pores are occurring is assessed.