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Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
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Multi-layered folding with voids.

T J Dodwell1, G W Hunt, M A Peletier

  • 1Department of Mechanical Engineering, University of Bath, UK. tjd20@bath.ac.uk

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Summary
This summary is machine-generated.

Mechanical properties and layering geometry compete in layered materials. External pressure drives trade-offs, creating striking periodic patterns in geological strata and paper stacks.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Geophysics

Background:

  • Layered materials deform due to competing mechanical properties and geometric constraints.
  • Voids form with smooth layers; curvature singularities arise from close packing.
  • External pressure influences deformation by penalizing voids, leading to complex patterns.

Purpose of the Study:

  • To model geometrically nonlinear multi-layered structures under axial loading and pressure confinement.
  • To analyze the trade-offs between mechanical properties and geometry in layered material deformation.
  • To investigate the emergence of periodic patterns in compressed layered systems.

Main Methods:

  • Constructed a simple model for multi-layered structures with non-interpenetration conditions.
  • Characterized energy minimizers via fourth-order nonlinear differential equations and contact-force Lagrange multipliers.
  • Numerically solved a fourth-order free-boundary problem to analyze solutions.

Main Results:

  • Identified energy minimizers as solutions to a free-boundary problem.
  • Demonstrated that external pressure forces a trade-off between voids and curvature.
  • Observed striking periodic patterns resulting from these competing effects.

Conclusions:

  • The model accurately captures the complex deformation behavior of layered materials.
  • Periodic patterns are a consequence of the interplay between geometry, mechanics, and external pressure.
  • Numerical solutions align with experimentally observed periodic patterns in layered systems.