Modelling Porous Plates with in-plane Functionally Graded Distribution of Porosity Using Classical and Non-classical Theories

Porous materials have emerged as pivotal components in various engineering applications due to their lightweight nature, high specific surface area, and customisable properties. In recent decades, porous materials have been widely used in many industrial sectors, including aerospace, civil engineering, and biomedical applications such as porous implants and meshes for guided bone regeneration. Functionally graded (FG) porous structures, with a graded porosity distribution, represent a particularly intriguing subset, offering tailored mechanical properties across spatial gradients . The mechanical behaviours of porous FG structures are of interest in the current literature in terms of static, vibration, and buckling problems, specifically in beams, plates, and shells. In the present work, non-classical micropolar and Cauchy continua are adopted to model porous plates with in-plane functionally graded distribution of porosities. First, through a multiscale procedure, the material constants of the equivalent micropolar/Cauchy homogenous model are determined for the heterogeneous plates with uniform porosities. The acquired data for various porosities is subsequently used to derive the function for each material parameter with regard to the pore size. The established homogenised model provides an efficient framework for investigating the mechanical response of porous plates with diverse porosity distributions, including 'V', 'A', 'X', and 'O'. To evaluate the applicability of the method, the displacement fields obtained from the homogenised equivalent models are compared to the response of the porous structure for a wide range of aspect ratios. The results show that for aspect ratios (width/height) around less than 1.3, functional porosity is important in predicting the correct mechanical response of the plate; however, as the aspect ratio increases, the overall porosity of the plate takes precedence and the distribution loses importance.