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Complex ordered patterns in mechanical instability induced geometrically frustrated triangular cellular structures.

Sung Hoon Kang1, Sicong Shan1, Andrej Košmrlj2

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Summary
This summary is machine-generated.

Geometrical frustration in triangular cellular structures surprisingly leads to ordered patterns when buckling occurs. Controlling porosity allows tuning these complex, ordered states, revealing the importance of connected geometry.

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Area of Science:

  • Materials Science
  • Mechanics of Materials
  • Complex Systems

Background:

  • Geometrical frustration, where local order cannot propagate due to constraints, often results in disordered states.
  • This phenomenon is significant in various physical and engineered systems.
  • Understanding frustration is key to designing materials with specific properties.

Purpose of the Study:

  • To investigate the behavior of buckling-induced geometrically frustrated triangular cellular structures.
  • To explore how geometrical constraints and buckling influence pattern formation.
  • To determine if ordered patterns can emerge from frustration and how they can be controlled.

Main Methods:

  • Theoretical modeling of triangular cellular structures under buckling conditions.
  • Experimental fabrication and testing of these structures.
  • Analysis of pattern formation as a function of porosity and geometry.

Main Results:

  • Buckling in these structures unexpectedly induces complex ordered patterns, contrary to typical frustration outcomes.
  • The resulting ordered patterns are tunable by adjusting the porosity of the cellular structures.
  • The connected geometry of the cellular network is identified as a critical factor in generating these ordered states.

Conclusions:

  • Geometrical frustration in triangular cellular structures does not necessarily lead to disorder.
  • Buckling can be harnessed to create tunable, ordered patterns in frustrated systems.
  • The design of connected geometries is crucial for controlling emergent order in frustrated materials.