3,472 research outputs found
Folding a Paper Strip to Minimize Thickness
In this paper, we study how to fold a specified origami crease pattern in
order to minimize the impact of paper thickness. Specifically, origami designs
are often expressed by a mountain-valley pattern (plane graph of creases with
relative fold orientations), but in general this specification is consistent
with exponentially many possible folded states. We analyze the complexity of
finding the best consistent folded state according to two metrics: minimizing
the total number of layers in the folded state (so that a "flat folding" is
indeed close to flat), and minimizing the total amount of paper required to
execute the folding (where "thicker" creases consume more paper). We prove both
problems strongly NP-complete even for 1D folding. On the other hand, we prove
the first problem fixed-parameter tractable in 1D with respect to the number of
layers.Comment: 9 pages, 7 figure
The relaxed-polar mechanism of locally optimal Cosserat rotations for an idealized nanoindentation and comparison with 3D-EBSD experiments
The rotation arises as the unique orthogonal
factor of the right polar decomposition of a given
invertible matrix . In the context of nonlinear elasticity
Grioli (1940) discovered a geometric variational characterization of as a unique energy-minimizing rotation. In preceding works, we have
analyzed a generalization of Grioli's variational approach with weights
(material parameters) and (Grioli: ). The
energy subject to minimization coincides with the Cosserat shear-stretch
contribution arising in any geometrically nonlinear, isotropic and quadratic
Cosserat continuum model formulated in the deformation gradient field and the microrotation field . The corresponding set of non-classical energy-minimizing
rotations represents a new relaxed-polar mechanism.
Our goal is to motivate this mechanism by presenting it in a relevant setting.
To this end, we explicitly construct a deformation mapping
which models an idealized nanoindentation and compare the corresponding optimal
rotation patterns with experimentally
obtained 3D-EBSD measurements of the disorientation angle of lattice rotations
due to a nanoindentation in solid copper. We observe that the non-classical
relaxed-polar mechanism can produce interesting counter-rotations. A possible
link between Cosserat theory and finite multiplicative plasticity theory on
small scales is also explored.Comment: 28 pages, 11 figure
Geometry, mechanics and actuation of intrinsically curved folds
We combine theory and experiments to explore the kinematics and actuation of
intrinsically curved folds (ICFs) in otherwise developable shells. Unlike
origami folds, ICFs are not bending isometries of flat sheets, but arise via
non-isometric processes (growth/moulding) or by joining sheets along curved
boundaries. Experimentally, we implement both, first making joined ICFs from
paper, then fabricating flat liquid crystal elastomer (LCE) sheets that morph
into ICFs upon heating/swelling via programmed metric changes. Theoretically,
an ICF's intrinsic geometry is defined by the geodesic curvatures on either
side, . Given these, and a target 3D fold-line, one can construct
the entire surface isometrically, and compute the bending energy. This
construction shows ICFs are bending mechanisms, with a continuous family of
isometries trading fold angle against fold-line curvature. In ICFs with
symmetric , straightening the fold-line culminates in a
fully-folded flat state that is deployable but weak, while asymmetric ICFs
ultimately lock with a mechanically strong finite-angle. When unloaded,
freely-hinged ICFs simply adopt the (thickness independent) isometry that
minimizes the bend energy. In contrast, in LCE ICFs a competition between flank
and ridge selects a ridge curvature that, unusually, scales as .
Finally, we demonstrate how multiple ICFs can be combined in one LCE sheet, to
create a versatile stretch-strong gripper that lifts 40x its own weight.Comment: The supplemental movies are available at
https://drive.google.com/drive/folders/1CR5TdbZNhveHiDYt0_a20O7_nQYS6xZ
A variational approach to necklaces formation in polyelectrolytes
By means of a variational approach we study the conditions under which a
polyelectrolyte in a bad solvent will undergo a transition from a rod-like
structure to a ``necklace'' structure in which the chain collapses into a
series of globules joined by stretched chain segments.Comment: 6 pages, 4 figures (unfortunately big). Requires revtex, eps
Mechanical Failure of a Small and Confined Solid
Starting from a commensurate triangular thin solid strip, confined within two
hard structureless walls, a stretch along its length introduces a rectangular
distortion. Beyond a critical strain the solid fails through nucleation of
"smectic"-like bands. We show using computer simulations and simple density
functional based arguments, how a solid-smectic transition mediates the
failure. Further, we show that the critical strain introducing failure is {\em
inversely} proportional to the channel width i.e. thinner strips are stronger!Comment: 6 pages, 7 figures, to be published in Indian Journal of Physics (in
press) as a Conference proceeding of CMDAYS-0
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