Automatic micro-scale modelling and evaluation of effective properties of highly porous ceramic matrix materials using the scaled boundary finite element method

Abstract

This paper presents an approach to the numerical estimation of effective properties of highly porous materials based on the scaled boundary finite element method (SBFEM). The latter can be formulated on quadtree meshes with hanging nodes and thus facilitates the efficient mesh generation and analysis of a large number of randomly created samples. To generate the corresponding Representative Volume Elements (RVEs), an improved Random Sequential Addition (RSA) method with overlap is used. Moreover, an alternative image-based digital matrix method for generating random assemblies of circular particles of the same size is proposed. In addition, a modified smoothing algorithm to treat the staircase boundaries present in a quadtree mesh is developed in order to accurately and efficiently capture the sinter-neck features of overlapping circular particles. The proposed image-based mesh generation and analysis procedure is used to evaluate the relationship between microstructural parameters and effective Young’s modulus considering a large number of samples. In this context, a new dimensionless morphological parameter Nfc is proposed. The latter represents the morphology and connectivity of voids and is shown to be a useful indicator with respect to the effective elastic properties of highly porous ceramic matrix material.