Berlin 2018 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 25: Statistical Physics II (General)
DY 25.8: Talk
Tuesday, March 13, 2018, 12:00–12:15, BH-N 243
Geometric frustration in non-periodic mechanical metamaterials — •Erdal C. Oğuz1, Anne Meeussen2,3, Martin van Hecke2,3, and Yair Shokef1 — 1School of Mechanical Engineering and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel — 2Huygens-Kamerlingh Onnes Laboratory, Universiteit Leiden, PO Box 9504, 2300 RA Leiden, the Netherlands — 3AMOLF, Science Park 104, 1098 XG Amsterdam, the Netherlands
We investigate geometric frustration in two-dimensional lattice-based mechanical metamaterials comprised of anisotropic triangular building blocks T, where each such T possesses a nontrivial floppy mode of deformation. When each triangle is oriented randomly neighboring triangles typically cannot deform self-consistently. On the one hand, we analyze the conditions under which a non-periodic packing of these blocks form compatible and frustration-free large-scale structures, i.e., structures that exhibit a global floppy mode that is compatible with the local deformations of each T. By mapping to an antiferromagnetic Ising model, we find an extensive number of possibilities to construct a compatible structure: (Ω0 ∼ exp(T)). On the other hand, we study incompatible metamaterials in detail and we reveal two distinct types of source of frustration (defects) which either highly localize the frustrated region to a small and finite domain (local defects) or cause delocalized and long-ranged multi-stable conflicts (topological defects) whose multi-stability scales as Ω ∼ exp(√T).