Department of Mechanics
Faculty of Civil Engineering
Czech Technical University (CTU)
Proposed originally as a visual aid for proving theorems in mathematical logic, Wang tilings have found subsequent applications in computer graphics, statistical physics, or biological computing. In this talk, we discuss the use of Wang tilings in designing, manufacturing, and self-assembling architectured (meta)materials.
The talk splits into four parts. The first part addresses the tiling concept in its most straightforward installment. It employs a single parent tile, possibly rotated by 90 degrees, allowing assembling structures with a locally-controlled Poisson ratio.
In the second part, we show that the elementary scenario naturally extends to the framework of vertex-based Wang tilings and demonstrate its use in designing a soft porous metamaterial with a non-periodic structure. Here, the emphasis is put on the inherent modularity of this concept and its potential for scalable robot-assisted manufacturing.
The third part of the talk is devoted to exploring the potential of Wang tiling formalism in centimeter-scale passive self-assembly of target patterns. To this purpose, we present a design principle for magneto-mechanical tiles that self-assemble in a checkerboard pattern under external mechanical excitation while exhibiting robust error-correcting features during the self-assembly process. Finally, the intrinsic limitations of this approach are discussed, along with a simulation-supported strategy for increasing the size of self-assembled patterns.
If time permits, in the fourth part, we summarize related developments in microstructure modeling, simulations, and topology optimization on non-periodic heterogeneous materials with Wang tilings, to highlight their broad applicability in multi-scale materials modeling.
This work was supported by the Czech Science Foundation project No. 19-26143X.
Dr. Jan Zeman is a Full Professor in the Theory of Materials and Structures at the Department of Mechanics, Faculty of Civil Engineering, Czech Technical University (CTU) in Prague.
Currently a core member of CTU’s Open Mechanics Group, Jan Zeman earned his Ing. (MSc. equivalent) degree in 2000 and his Ph.D. in 2003 from CTU in Civil Engineering with a specialization in Structural Mechanics. He received the 2000 Hlavka Talent Foundation prize (top CTU student) and the Ivo Babuška Award for the best Ph.D. thesis in Applied and Computational Mathematics and Mechanics in 2003.
Jan’s research interests lie at the interface between applied mechanics and mathematics, with an emphasis on modeling and simulation of deterministic and stochastic microstructured materials, variational techniques for modeling inelastic materials, and mathematical analysis of engineering models and algorithms in general. His early work was supported in the context of a Marie-Curie Intra-European Fellowship (2005), and, in addition to leading 5 projects funded by the Czech Science Foundation (CSF) from 2004 to 2019, he is currently the principal investigator of a highly-selective five-year EXPRO project, a CSF initiative established in 2019, aiming at the computer-aided design of modular architectured materials. In addition to research, he is committed to mentoring talented future researchers and has (co-)supervised 8 doctoral students (1 ongoing).