Abstract
The main advantage of the Wang tiling concept for material engineering is ability to create large material domains with a relatively small set of tiles. Such idea allows both a reduction of computational demands and preserving heterogeneity of a reconstructed media in comparison with traditional cell concepts. This work is dealing with a random heterogeneous material composed of monodisperse circular hard particles within a matrix. The Wang tile sets are generated via algorithm with molecular dynamics and adaptive boundaries approach. Even though previous works proved usefulness of the Wang tiling for material reconstruction, still plenty of questions remain unanswered. In here we would like to provide simulations with emphasis on the overall particle distribution and the ratio of hard disc number to tile size. The results and discussion should followers help with settings of both tile generations and the tiling algorithms when creating samples of various degree of heterogeneity.
Highlights
Despite the exponentially increasing computing power, simulations and modelling of random heterogeneous materials on microscale have been performed mostly using the periodical unit cells (PUCs) forming a representative sample
Within last few years a group of researches has been dealing with the Wang tiling approach as a tool for random heterogeneous material modelling
The pilot work [3] linking the Wang tile principles with material engineering, utilized static approach, whereas in this paper a process based on the molecular dynamics is utilized
Summary
Despite the exponentially increasing computing power, simulations and modelling of random heterogeneous materials on microscale have been performed mostly using the periodical unit cells (PUCs) forming a representative sample. The last tiling is made of the set with 36 particles per tile, but finial domain exhibits the same fraction as well It is obvious, that the first simulation represents S arrangement, whereas the second and the third tiling form rather R arrangement (particles randomly over whole area) [4]. The main goal of the presented contribution is to provide some simulations and build up recommendations for particle-tile size relation with emphasis on overall arrangement and different states of heterogeneity/ordering. These suggestions should help followers with the settings of a generation algorithm when tiling a material model with required geometrical properties. In the conclusion the summary of the paper with possible ways of the future work is presented
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