Wang Tiles Local Tilings Created by Merging Edge-Compatible Finite Element Meshes

Abstract

Abstract. In this contribution, we present the concept of Wang Tiles as a surrogate of the periodic unit cell method (PUC) for modelling of materials with heterogeneous microstructures and for synthesis of micro-mechanical fields.The concept is based on a set of specifically designed cells that compresses the stochastic microstructure into a small set of statistical volume elements -tiles. Tiles are placed side by side according to matching edges like in a game of domino. Opposite to the repeating pattern of PUC the Wang Tiles method with the stochastic tiling algorithm preserves the randomness for reconstructed microstructures. The same process is applied to obtain the micro-mechanical response of domains where the evaluation as one piece would be time consuming. Therefore the micro-mechanical quantities are evaluated only on tiles (with surrounding layers of tiles of each addressed tile included into the evaluation) and then synthesized to the micro-mechanical field of whole domain.