Microstructural modelling of functionally graded materials using stochastic Voronoi diagram and B-Spline representations

Abstract

Functionally graded materials (FGMs) have been extensively studied in the past few decades. An overwhelming majority of existing investigations are based on the compositional heterogeneity model where the material distributions/volume fractions characterised at macroscopic scale are primary concerns. In contrast to the extant FGM modelling approaches, this article presents a new approach to modelling the microstructures of FGMs. A novel digital model based on the stochastic Voronoi diagram and B-Spline representation is proposed. We demonstrated that, using the proposed microstructural FGM model, FGMs with generic and customisable microstructures can be easily designed, meanwhile the irregular topology or complex network that are commonplace in nature can be properly represented. The proposed modelling approach facilitates the design of FGM with natural and realistic microstructures, and, more importantly, it does not require expensive imaging equipment in the design process, and digital models can be constructed at interactive or quasi-interactive rate. With two case studies, we show that efficient downstream design validations or response simulations can be conveniently conducted.