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Optimized Wang Tiles Generation for Heterogeneous Materials Modelling

The paper deals with a modelling of random heterogeneous materials composed of circular solid particles within a matrix. The concept of Wang tiling is utilized to generate material patterns. Wang tiling principles enable to create random heterogeneous structures with high reduction of periodicity artefacts in comparison with the traditional approach of the Periodic Unit Cell (PUC). A packing algorithm based on molecular dynamics for Wang tiles generation is introduced. During the process of generation particles grow, move and collide with tile edges and with each other in order to achieve required or optimal particle placements without an overlapping. A set of Wang tiles include eight different tiles with specific boundary conditions which allow composing of random heterogeneous materials applying a stochastic tiling algorithm. An optimization technique based on the Particle Swarm Optimization (PSO) is utilized to get a material model with similar statistical information compared with a reference pattern. Due to the nature of investigated materials the Radial Distribution Function (RDF) was chosen as a tool for statistical description.