"55940" . "For many materials the size of Representative Volume Element may be well beyond conventional dimensions. We propose a microstructure compression technique based on Wang tilings that allows to quickly generate large numbers of microstructure realizations of arbitrary sizes while preserving spatial characteristics of the reference system. The microstructure spatial information is compressed within a set of Wang tiles, square tetraminoe like cells with codes assigned to edges. The edges are designed in a specic way allowing an assembly of tiles into tilings that guarantee conformity of the carried information across the tilling lattice. Having the microstructure compression at hand, it allows to investigate optimal dimensions of Representative Volume Elements for various physical phenomena in an extremely ecient way. The attention is limited to linear elasticity in this work. Moreover, we discuss the potential enhancement to the analysis through taking the advantage of regular nature of the tiling lattice, such as it invokes the application of domain decomposition techniques. Alternative remarks on tiles treated as macroelements in order to reduce number of DOFs are also presented."@en . . "2"^^ . "[C763DA1789DF]" . . . . "Do\u0161k\u00E1\u0159, Martin" . . "2"^^ . . . "Wang Tilings for Modelling of Heterogeneous Materials" . "RIV/68407700:21110/14:00219553!RIV15-GA0-21110___" . "Wang tiling; homogenization; microstructure synthesis"@en . . "http://publications.lib.chalmers.se/publication/202188-proceedings-of-14th-european-mechanics-of-materials-conference-emmc14" . . . "P(GA13-24027S)" . "Wang Tilings for Modelling of Heterogeneous Materials"@en . "Wang Tilings for Modelling of Heterogeneous Materials" . "Nov\u00E1k, Jan" . . . "Wang Tilings for Modelling of Heterogeneous Materials"@en . . "RIV/68407700:21110/14:00219553" . . "21110" . "For many materials the size of Representative Volume Element may be well beyond conventional dimensions. We propose a microstructure compression technique based on Wang tilings that allows to quickly generate large numbers of microstructure realizations of arbitrary sizes while preserving spatial characteristics of the reference system. The microstructure spatial information is compressed within a set of Wang tiles, square tetraminoe like cells with codes assigned to edges. The edges are designed in a specic way allowing an assembly of tiles into tilings that guarantee conformity of the carried information across the tilling lattice. Having the microstructure compression at hand, it allows to investigate optimal dimensions of Representative Volume Elements for various physical phenomena in an extremely ecient way. The attention is limited to linear elasticity in this work. Moreover, we discuss the potential enhancement to the analysis through taking the advantage of regular nature of the tiling lattice, such as it invokes the application of domain decomposition techniques. Alternative remarks on tiles treated as macroelements in order to reduce number of DOFs are also presented." . . .