A circle/sphere populating method to generate 2D/3D stochastic microstructures

Abstract

A circle/sphere populating method is proposed to generate 2D/3D stochastic microstructures. The proposed method uses circles/spheres as the basic elements and generates microstructure features through the populating process of the circles/spheres. In the populating process, the cores are first generated randomly and circles/spheres start to populate around the cores or the previous generation’s circles/spheres. The populating process is controlled by the input parameters including the volume fraction, core number, circle/sphere size distribution, circle/sphere populating distance distribution, circle/sphere populating number, and populating direction constraint angle. The proposed method was compared with the QSGS method and random circle/sphere method in 2-dimensional (2D) and 3-dimensional (3D) cases. The proposed method shows advantages in generating microstructures with clear feature geometries and boundaries. Furthermore, parametric studies are conducted in 2D and 3D to investigate the effect of input parameters on the generated microstructures. With the consideration of circle/sphere spatial distributions, the proposed method can achieve different degrees of feature clustering and agglomerating. A wide range of microstructure morphologies can be achieved by adjusting the input parameters. A more accurate description of the features in the microstructures can be achieved without the involvement of the annealing-based optimization process. As a case study, the proposed method was used to generate sandstone microstructures with different grain size distributions and spatial distributions, and the permeability of generated sandstone was analyzed. Furthermore, the proposed method was applied to generate the microstructure model with a target radial distribution function to demonstrate its computational efficiency by comparing it with the random sphere method and simulated annealing based method.