Foldable Auxe,cs Materials Burhan Saifaddin Advisor: Prof. L. Mahadevan Applied Math Lab.
Folding in Nature: Protein Folding from random coil (wikipedia) Extreme Mechanics Geological fold in Poland. Manufacturing : Microrobo,cs Lab Whiteside Lab What Drives Blooming, or Leaves shape ? Liang and Mahadevan. Growth, geometry, and mechanics of a blooming lily. ONAS 2011 Incorporate foldable structure with electronics Biological Tissues : Gut, intes,ne, brain folds Adv. Funct. Mater. 2010, 20, 28–35 Savin et al. On the growth and form of the gut. PNAS 2011
lgorithms of resolution of the individual elements (tiles) and the number of gning the elements that can be effectively combined in a single sheet. First, an object the resolution of the tiles is limited by the scalability of eachhe stickers element. The current materials and methods use to create the substrate can be reasonably shrunk to create tiles on the order Folding in Manufacturing and Engineering of a few millimeters in largest dimension. Below this threshold, lithography and micromolding techniques (for example, molding described elastomers using capillary action (25)) could be used to reducety-two-tile feature sizes further. Scaling of actuation has two considerations: Folding in Engineering : Foldable Robo,cs Foldable Solar Cells Foldable BaZeries Paper Based Electronics ….. own in lower right—mm:ss.s) of a self-folding “boat.”(A). All actuators receiving currentboat on side (D). Programmable Magne,c Self-‐assembly Hawkes et al. PNAS ∣ July 13, 2010 ∣ vol. 107 ∣ no. 28 ∣ Appl. Phys. Lett. 96, 071902 ͑2010͒ 071902-2 Myers, Bernardi, and Grossman Appl. Phys. Lett. 96, 071902 ͑2010͒ hematics of 3DPV structures: ͑a͒ GA-optimized Foldable 3DPV 4 triangles inside the bounding box; ͑b͒ funnel, a GA-optimized structures that retains their supe- Solar Cells Inexpensive Deployment of Solar Cells FIG. 2. ͑Color online͒ Schematics of 3DPV structures: ͑a͒ GA-optimized structure shown with all 64 triangles inside the bounding box; ͑b͒ funnel, aer shapes. More than 2/3 of the cost of PV systems is simpliﬁed version of most GA-optimized structures that retains their supe- rior performance over other shapes.gredients ofMarch 15, 2005 vol. 102 no. 11 PNAS the complicated GA struc- in deployment cost. contains most key ingredients of the complicated GA struc- tures.e energy generated byppl. Phys. LeZ. 96, 071902, 2010 Myers, et al. A simple open-box We compared the energy generated by simple open-boxl structures through a ﬁgure of merit M, shapes and the funnel structures through a ﬁgure of merit M,
How Auxe,cs (NPR) Materials work news and views Unstretched Stretched Daedalus a The a ν = –et/el = –(ΔD/D)/ (ΔL/L) The librar only by co b crumbling So Daedal Two dimensional structures: closed boo should be books ont transfer th a) Honycomb cells A pape typical inf of fibres o should be b) Inverted honycomb cells wavelengt wavelengt Figure 1 Positive and negative Poisson’s ratios. Stretching these two-dimensional hexagonal distinguis structures horizontally reveals the physical origin of Poisson’s ratio. a, The cells of regular side. A pu Miura-‐ori fold honeycomb or hexagonal crystals elongate and narrow when stretched, causing lateral contraction and so a positive Poisson’s ratio. b, In artificial honeycomb with inverted cells, the structural launched or bottom elements unfold, causing lateral expansion and a negative Poisson’s ratio. simultane page only, Proper,es: so the overall Poisson’s ratio is almost always membranes. The overall elasticity of a cell page was a positive. membrane results from both the protein A suffi Absorb Energy, resist fracture. The elastic behaviour of the membranes skeleton and the high lipid content, but the trace a sin studied by Bowick et al.1 is said to be ‘uni- relative contributions are not yet known. letters fro versal’ because the authors require only a Even so, Bowick and colleagues’ results are Some applica,ons: body armor, an opaque sparse set of assumptions to predict the provocative. If our usual expectations about absorb th Poisson’s ratio. They start with a simple net- how things deform do not apply to biological shock absorber, packing material, sharp atte work of nodes, resembling a fishing net with membranes then we may need to reconsider or ‘echo’ c , fixed connections, which they model using the influence of membrane mechanics7 on letter. A b knew and elbow pads, sponge a Monte Carlo simulation. Bowick et al. the shape of cells, the formation of vesicles, the stream show that a negative Poisson’s ratio is a uni- and the deformation of cells during life photocell mops. versal property of such systems, whether the processes. For example, red blood cells are Unfort membrane is dominated by rigid bonds that routinely deformed when they pass through both sides resist bending or by ‘self-avoiding’ inter- fine blood capillaries. As they deform, the may be insilver.neep.wisc.edu/~lakes/Poisson.html atomic forces that prevent portions of the membrane skeleton can unfold, which both of wh structure overlapping. This unusual form of elasticity may also Metallic Foam might help to transport large molecules or expose reactive chemical groups. Similar But this is come in. E
Poisson Ra,o is a very important mechanical REVIEW ARTICLE NATURE MATERIALS DOI: 10.1038/NMAT3134 proper,es a 0.6 Liquids Lead Rubber 0.4 Dental composites Metallic glasses Steel ty Gels Oxide glasses i tiv 0.2 Concrete Zeolites c Cartilage ne Bone Honeycomb in g on 0.0 Cork Gases dc ck pa e Carbon nanotube Laminates as er re sheets ns –0.2 Inc De α-cristobalite Unscreened metals Bi, As –0.4 Laser-cooled crystals Colloidal crystals –0.6 Re-entrant polymer foams –0.8 Critical ﬂuids –1.0 –1.2 0.001 0.01 0.1 1 10 100 B/G b Bulk modulus B c bulk modulus B BMG hange in size -‐ c • ν = [3(B/G – 2)]/[6(B/G + 2)] 400 fcc Unstable by domain Rubbery Stiff 350 shear modulus G – change in shape Ductile bcc ν = 1/2 ν = 0.3 Brittle ν = [1⁄2(Vt/Vl)2 – 1]/[(Vt/Vl)2 – 1] formation • 300 B/G = 2.4 hcp Stable • isotropic range of –1 ≤ ν ≤ 1⁄2 for 0 ≤ B/G < ∞ at small strains 250 B (GPa) ν=0 Fe– 450 Ni– Unreachable • Nonlinear regime ν < -‐1. Spongy Anti-rubbery 200 Pd– Ideal isotropic solid Dilational ν = –1 150 Cu– B/G = 5/3 Auxetic Foam Structures wν2= –2 Nega*ve Poisssons Ra*o. Lakes. science. 1987. ν = ith a Shear modulus G 100 RE- fcc metals –4G/3 < B < 0 Zr– bcc metals Unstable by volume change ν=1 50 hcp metals Poisson’s ra*o and modern materials. Nature Materials. G. N. Greaves, but stable if constrained Mg– A. L. Greer, R. S. Lakes and T. Rouxel 24 Oct 2011 0 0 50 100 150 200 250
Project • Make Mouri-‐Ori Fold. • Vary angle to vary mechanical proper,es. • How does the rela,on look like. • Measure Poisson ra,os. Miura-‐ori paZern is a Rhomboidal (2 angles , 2 lengths). • They developed computa,onal tool to simulate the stretching, bending and folding of thin sheets of material to predict its mechanical proper,es. Pleated and Creased Structures. Levi Dudte, Zhiyan Wei, L. Mahadevan. APS 2012 Mee,ng. 2:30 PM–5:30 PM, Tuesday, February 28, 2012 Room: 153C
Possion ra,o measurements Strain Vs. strain plots for SU-‐8 microstructures to measure NPR (no varying of angles) ~100 μm Adv. Mater. 1999, 11, No. 14
Acknowledgment • Applied Math Lab – Advisor and PI: L. Mahadevan – Levi Dudte – Zhiyan Wei • Microrobo,cs Lab – PI: Robert Woods – Lab Manger: Michael Smith.
Inﬂuence of membrane mechanics on Cells shape
Problems faced • Project start Monday, Feb 6 2012: 17 days only and talked to students much later. • No sotware access (Corel Draw, AutoCAD) • Hard access to Laser Lab • Access to lab to measure passion ra,o.
Tensile Tes,ng structures to measure the Poissons Ra,o