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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 Shokef11School 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: (Ω0exp(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).

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