The paper presents a concept to compress and synthesize complex material morphologies that is based on Wang tilings. Specifically, a microstructure is stored in a set of Wang tiles and its reconstruction is performed by means of a stochastic tiling algorithm. A substantial part of the study is devoted to the setup of optimal parameters of the automatic tile design by means of parametric studies with statistical descriptors at heart. The performance of the method is demonstrated on four two-dimensional two-phase target systems, monodisperse media with hard and soft disks, sandstone, and high porosity metallic foam.

Department of Mechanics Faculty of Civil Engineering Czech Technical University Prague Thákurova 7 166 29 Praha Czech Republic

Department of Mechanics Faculty of Civil Engineering Czech Technical University Prague Thákurova 7 166 29 Praha Czech Republic and Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Veveří 95 331 602 00 Brno Czech Republic

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Bounded Wang tilings with integer programming and graph-based heuristics