Dynamics of Miura-patterned foldable sheets in shear flow

Area of Science:

• Fluid Dynamics
• Mechanics of Materials
• Origami Engineering

Background:

• Piecewise rigid sheets with crease lines behave like hinged joints.
• Miura-pattern sheets tessellate into parallelograms, folding from planar to compact states.

Purpose of the Study:

• To analyze the dynamics of Miura-pattern sheets in shear flow.
• To characterize the terminal states of sheet motion under hydrodynamic forces.

Main Methods:

• Modeling hinged sheets as constrained multibody systems (inertia-less).
• Calculating hydrodynamic drag using inscribed elliptic disks, neglecting intra-panel interactions.

Main Results:

• Symmetric motion leads to periodic tumbling/breathing (limit cycle) or complete unfolding (steady state).
• Asymmetric motion results in steady states, periodic tumbling, quasiperiodic orbits, or resonant quasiperiodic orbits.
• No chaotic dynamics were observed for the studied Miura-sheet configurations.

Conclusions:

• Miura-pattern sheets in shear flow demonstrate predictable dynamics, settling into stable or periodic states.
• The folding angle and symmetry dictate the sheet's long-term behavior in flow.
• Hydrodynamic interactions significantly influence the folding dynamics of such structures.