The peridynamic model.

<p>(a) A small, randomly selected region in the distal membrane is represented as a collection of particles (small circles). Each particle represents a collection of lipid molecules, and is located at the center of a circular neighborhood (N_x). The motion of an arbitrary particle x (in yellow) at the center of N_x is influenced by the motion of every particle in N_x via bonds. If no forces apply to the membrane, the particles in N_x are considered to be in an undeformed state. The close-up shows vector ξ, representing the distance between bonded particles x and x’, where T is the force vector state that existed prior to the bond being broken. (b) As tension increases, the particles move apart from each other and the corresponding bonds stretch. At some critical value of stretch, the distance between the center particle (yellow dot) and some number of neighboring particles becomes too large, leading to broken bonds and disconnected particles (x', white dots). This corresponds to the rupture (pore) formation among membrane lipids.</p

DataSheet1_Curvilinear Kirigami Skins Let Soft Bending Actuators Slither Faster.pdf

The locomotion of soft snake robots is dependent on frictional interactions with the environment. Frictional anisotropy is a morphological characteristic of snakeskin that allows snakes to engage selectively with surfaces and generate propulsive forces. The prototypical slithering gait of most snakes is lateral undulation, which requires a significant lateral resistance that is lacking in artificial skins of existing soft snake robots. We designed a set of kirigami lattices with curvilinearly-arranged cuts to take advantage of in-plane rotations of the 3D structures when wrapped around a soft bending actuator. By changing the initial orientation of the scales, the kirigami skin produces high lateral friction upon engagement with surface asperities, with lateral to cranial anisotropic friction ratios above 4. The proposed design increased the overall velocity of the soft snake robot more than fivefold compared to robots without skin.</p

Effect of Wrinkles on the Surface Area of Graphene: Toward the Design of Nanoelectronics

Graphene has attracted intense attention to the use in extreme applications. However, its small thickness facilitates wrinkle formation, and it is not clear how such structural change affects its area-specific capacitance. Herein, we combine molecular dynamics and continuum mechanics-based simulations to study the changes in surface area induced by wrinkles. We find that the high specific surface area of graphene can only be affected up to 2% regardless of loading conditions, geometry, and defects

Illustration of a helix (top), a hemihelix with one perversion marked by an arrow (middle) and a hemihelix with multiple perversions (bottom).

<p>The scale bar is 5 cm, and is the same for each image. These different shapes were all produced in the same way as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093183#pone-0093183-g002" target="_blank">figure 2</a> with the same value of pre-strain but with decreasing values of the height-to-width ratio of the bi-strip's cross-section. , , ).</p

Video1_Curvilinear Kirigami Skins Let Soft Bending Actuators Slither Faster.MP4

The locomotion of soft snake robots is dependent on frictional interactions with the environment. Frictional anisotropy is a morphological characteristic of snakeskin that allows snakes to engage selectively with surfaces and generate propulsive forces. The prototypical slithering gait of most snakes is lateral undulation, which requires a significant lateral resistance that is lacking in artificial skins of existing soft snake robots. We designed a set of kirigami lattices with curvilinearly-arranged cuts to take advantage of in-plane rotations of the 3D structures when wrapped around a soft bending actuator. By changing the initial orientation of the scales, the kirigami skin produces high lateral friction upon engagement with surface asperities, with lateral to cranial anisotropic friction ratios above 4. The proposed design increased the overall velocity of the soft snake robot more than fivefold compared to robots without skin.</p

Fractal dimension analysis of ruptures in actual membranes and simulations.

<p>(a-c) Binary images showing the contour of the fractal ruptures in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0165947#pone.0165947.g003" target="_blank">Fig 3O and 3R</a> (G = 5) and 4l (G = 7.5). (c) Plots showing the fractal dimension (D) of rupture patterns in (a),(b) and (c). The slope of the red line shows the fractal dimension of the pattern in panel a, D = 1.63, the pattern in panel (b), D = 1.70, and the pattern in c, D = 1.56. The circular rim forming around the expanding membrane in the simulations has been removed manually with image processing software. All fractal dimensions have been calculated by using the reticular cell counting (box counting) method. The plots show the relation between the number of occupied boxes (y-axes) and the box size. The fractals in biological membranes (not shown) feature D values around 1.7[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0165947#pone.0165947.ref001" target="_blank">1</a>]). The analysis from the simulations show that both slope and D are similar to the experimental values.</p

Transition in rupture morphology with increasing shear moduli.

<p>(a-l) The peridynamic simulations of the lipid membrane which is shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0165947#pone.0165947.g003" target="_blank">Fig 3</a> (j-l), but with gradually increased shear modulus. (a-d) The ruptures become rugged where G = 1 MPa. (e-h) The straight edges of the ruptures become more pronounced where G = 2.5 MPa and branches start to appear. (i-l) The ruptures appear as elongated finely branched structures where G = 7.5 MPa. These structures typically evolve into fractals(l). The color bar in (d) applies to all simulations shown in Fig 4, and is identical to the one in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0165947#pone.0165947.g003" target="_blank">Fig 3</a>. The number of pinning points in all simulations in this figure is 16, and the positions of the pinning sites are identical to the ones in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0165947#pone.0165947.g003" target="_blank">Fig 3J</a> and p (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0165947#pone.0165947.s004" target="_blank">S2 Movie</a>). The ratio of the diameter of the expanded membrane to the initial diameter (D/D₀) is shown below each snapshot of the simulations.</p

Video2_Curvilinear Kirigami Skins Let Soft Bending Actuators Slither Faster.mp4

The locomotion of soft snake robots is dependent on frictional interactions with the environment. Frictional anisotropy is a morphological characteristic of snakeskin that allows snakes to engage selectively with surfaces and generate propulsive forces. The prototypical slithering gait of most snakes is lateral undulation, which requires a significant lateral resistance that is lacking in artificial skins of existing soft snake robots. We designed a set of kirigami lattices with curvilinearly-arranged cuts to take advantage of in-plane rotations of the 3D structures when wrapped around a soft bending actuator. By changing the initial orientation of the scales, the kirigami skin produces high lateral friction upon engagement with surface asperities, with lateral to cranial anisotropic friction ratios above 4. The proposed design increased the overall velocity of the soft snake robot more than fivefold compared to robots without skin.</p

Growth rate as a function of the mode number for three different strips characterized by , , and .

<p>The growth rate is determined when the applied force decreases to .</p

The experiment.

<p>(a) Confocal laser scanning micrograph of a spreading double lipid bilayer membrane(DLBM), top view. (b) Schematic drawing of the DLBM in (a), side view. DLBM consists of a distal (upper, red color) bilayer and the proximal (lower, blue color) bilayer. The spreading edge of the double bilayer performs a 'tank-tread' motion. (c) Micrograph of a ruptured membrane. (d) Schematic drawing showing a rupture in the distal membrane. Upon rupturing, the lipid material migrates towards the edges onto the substrate.</p