(423c) Dynamics of Rigidly Foldable Sheets in Shear Flow

We study the dynamics of piecewise rigid sheets containing predefined crease lines in
shear flow. The crease lines act like hinge joints along which the sheet may
fold rigidly, i.e. without bending any other crease line. We choose the crease
lines such that they tessellate the sheet into a two-dimensional array of
parallelograms. When all the hinges are fully open the sheet is planar, whereas
when all are closed the sheet folds over itself to form a compact flat
structure. Such a tessellation is known as a `Miura`-pattern in the origami
community. Due to rigidity constraints the folded state of a `Miura`-sheet can
be described using a single fold angle.

We model a hinged sheet using the framework of constrained multibody systems in
the absence of inertia. The hydrodynamic drag on each parallelogram is
calculated based on an inscribed elliptic disk. We present results highlighting
the various modes of coupled tumbling and folding motion of the sheet.
Furthermore, when the joints are associated with a bending potential, we study
the buckling behavior of an intially planar sheet in shear flow.