Complex Ordered Patterns in Mechanical Instability Induced Geometrically Frustrated Triangular Cellular Structures

Abstract

Geometrical frustration arises when a local order cannot propagate throughout the space because of geometrical constraints. This phenomenon plays a major role in many systems leading to disordered ground-state configurations. Here, we report a theoretical and experimental study on the behavior of buckling-induced geometrically frustrated triangular cellular structures. To our surprise, we find that buckling induces complex ordered patterns which can be tuned by controlling the porosity of the structures. Our analysis reveals that the connected geometry of the cellular structure plays a crucial role in the generation of ordered states in this frustrated system.

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

“…In two dimensions, this rule can easily be satisfied on a square lattice, but not on a triangular one, so that the system becomes frustrated. While it has been shown that in periodic 2D beam lattices, geometric frustration favors the formation of complex ordered patterns [181] (see Fig. 15(b)), and in aperiodic architectures, it typically prevents a coherent and predictable response.…”

“…Building on these initial results, a library of 2D [21,174,180,181] and 3D [164] porous structures and structured porous shells [22,169,182] in which buckling induces pattern transformations has been identified (see Fig. 11).…”

Chiral structures from achiral liquid crystals in cylindrical capillaries

“…Recently and in a different vein, identification and elucidation of pathways by which achiral building blocks spontaneously organize to create chiral structures have become an area of active study. Examples of these pathways include packing with multiple competing length scales (8-10, 23, 24), reconfiguration through mechanical instabilities of periodic structures (20,25,26), and helix formation of flexible cylinders through inter-and intracylinder interactions (27,28). In addition, the system of a broken chiral symmetry often consists of domains of opposite handedness with defects separating the domains.…”

Vibrant times for mechanical metamaterials

“…1(e). In this sense, the metamaterial properties are programmable or reprogrammable [73] (also see [68,78,79] ). If the constituent material had an infinitely large stretching modulus, the Miura folding would exhibit only one degree of freedom [66,71] ; bistability could not occur.…”