Modelling Porous Plates with In-Plane Functionally Graded Porosity Distribution Using Classical and Non-Classical Theories: Application to Dental GBR Meshes

Porous materials have emerged as pivotal components in diverse engineering applications, such as biomedical, aerospace, and civil, due to their light weight, high surface area, and customisable properties. Functionally graded (FG) porous structures represent an intriguing subset, offering tailored mechanical properties across spatial gradients. In this study, non-classical micropolar and Cauchy continua are used to model porous plates with functionally graded porosities that are in the same plane. First, a homogenisation scheme is utilised based on strain energy equivalence to find the equivalent material properties. 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’ patterns, and for a broad range of aspect ratios. Results show that for aspect ratios less than approximately 1.5, the mechanical response of the FG porous structure depends highly on the functional porosity pattern. In this range, micropolar theory outperforms Cauchy theory in predicting the stiffness and displacement distribution of the FG porous structures. This method is used to study a type of dental implant called guided bone regeneration (GBR) mesh. The central part of the mesh has mechanical properties similar to trabecular bone, and the fixing areas are as close to cortical bone as possible to provide the needed load-bearing capacities while ensuring proper occlusivity.