A non-classical computational method for modelling functionally graded porous planar media using micropolar theory

Abstract

The current study proposes a computational-based method to employ the non-classical micropolar continuum for modelling plates with in-plane functionally graded porosities. Initially, a homogenisation method is developed to derive the micropolar parameters of porous heterogenous plates based on strain energy equivalence in various designed deformations simulated via finite element analysis. The modelling procedure is further augmented to accommodate structures with functionally graded porosities. The established method offers an effective framework for studying the mechanical behaviour of porous plates with various porosity distributions and a wide range of aspect ratios. Results indicate that the micropolar theory-based modelling surpasses traditional Cauchy theory in accurately predicting the stiffness and displacement distribution of the FG porous structures. The novelty of this study lies in the integration of micropolar theory with the homogenisation of graded porosity patterns, offering enhanced predictions for materials with microstructural features. Additionally, a custom finite element formulation is developed in COMSOL to implement micropolar elasticity, significantly improving the computational efficiency to account for complex geometry, loading, and boundary conditions. To show the applicability of the method, the modelling is used to design a dental implant with its functional property mimicking that of the natural bone to avoid stress-shielding while ensuring proper occlusivity.