Efficient mesh assisted placement algorithm for generation of random microstructures with custom inclusion shapes up to extremely high volume fractions

Abstract

Finite element analysis (FEA) of microstructural representative volume elements (RVEs) is a key component of modern research in composite materials with randomly distributed inclusions. The advent of machine learning techniques utilizing such FEA results have been instrumental in deriving new insights on microstructure-property relationships of stochastic composites. Training these ML models require a large number of diverse microstructures, but current algorithms face difficulties in generating RVEs with high volume fractions and complex inclusion morphologies. Here, we present a novel algorithm, Mesh Assisted Placement (MEAP), which employs a dynamic mesh grid within the bounding box to track the available space and accelerate the positioning of any custom-shaped inclusions. The inclusion boundaries are generated with splines, and an intersection-counting algorithm is used to prevent overlaps. Inclusion area and distribution were regulated with Gaussian integration and a propagation-based method respectively, to ensure adherence to user inputs. MEAP was assessed and found to give highly random inclusion distributions based on nearest neighbor orientation, Ripley’s K function, and the pair distribution function. It can produce RVEs up to a maximum volume fraction of > 90 %, with computational time up to 4 orders of magnitude faster than existing algorithms. Validation of MEAP was carried out by modelling the microstructures of heterogeneous materials from the literature (particulate metal-matrix composites, fiber-based CFRP and irregular carbides in low alloy steel), subjecting these microstructural models to FEA and comparing the simulated results with previously reported experimental results. In all cases, excellent agreement between the FEA and experimental results were obtained.