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A04 WADA, Hirofumi |Proposed Research Projects (2016-2017)

Paper | Original Paper

2017

Tomohiko G. Sano, Tetsuo Yamaguchi, and Hirofumi Wada,
Slip Morphology of Elastic Strips on Frictional Rigid Substrates,
Physical Review Letters 118, 178001 (2017).

[Summary] The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate isinvestigated by a combination of theory and experiment. We find a rich variety of morphologies, which—when the bending elasticity dominates over the effect of gravity—are classified into three distinct types ofstates: pinned, partially slipped, and completely slipped, depending on the magnitude of the vertical strainand the coefficient of static friction.We develop a theory of elastica under mixed clamped-hinged boundaryconditions combined with the Coulomb-Amontons friction law and find excellent quantitative agreementwith simulations and controlled physical experiments. We also discuss the effect of gravity in order tobridge the difference in the qualitative behaviors of stiff strips and flexible strings or ropes. Our study thuscomplements recent work on elastic rope coiling and takes a significant step towards establishing a unifiedunderstanding of how a thin elastic object interacts vertically with a solid surface.

2016

Yasuaki Morigaki, *Hirofumi Wada and *Yoshimi Tanaka,
Stretching an elastic loop: Crease, helicoid, and pop-out,
Physical Review Letters 117, 198003 (2016).

[Summary] Under geometric constraints, a thin structure can respond to an external loading in an unexpected way. A paper strip that is looped and pulled can be used for simple experimentation of such a process. Here, we study this seemingly very simple phenomenon in detail by combing experiments and theory. We identify the three types of shape transitions, i.e., crease, helicoid, and pop out, from a stretched loop, and classify them in terms of parameters characterizing a ribbon geometry. We establish a transition-type diagram by compiling our extensive experimental data. Numerical simulations based on the Kirchhoff rod theory and scaling argument reveal that the pop-out transition is governed by a single characteristic length ξ ∼ b2=h, where b and h are the ribbon’s width and thickness, respectively. We also reveal the key roles of other physical effects such as the anisotropy of the bending elasticity and plastic deformations upon the shape selection mechanisms of a constraint ribbon.

Daichi Matsumoto, Koji Fukudome and *Hirofumi Wada,
Two-dimensional fluid dynamics in a sharply bent channel: Laminar flow, separation bubble and vortex dynamics,
Physics of Fluids 28, 103608 (2016).

[Summary] Understanding the hydrodynamic properties of fluid flow in a curving pipe and channel is important for controlling the flow behavior in technologies and biome- chanics. The nature of the resulting flow in a bent pipe is extremely complicated because of the presence of a cross-stream secondary flow. In an attempt to disentangle this complexity, we investigate the fluid dynamics in a bent channel via the direct numerical simulation of the Navier-Stokes equation in two spatial dimensions. We exploit the absence of secondary flow from our model and systematically investigate the flow structure along the channel as a function of both the bend angle and Reynolds number of the laminar-to-turbulent regime. We numerically suggest a scaling relation between the shape of the separation bubble and the flow conduc- tance, and construct an integrated phase diagram.

Hirofumi Wada,
Structural mechanics and helical geometry of thin elastic composites,
Soft Matter 12, 7386-7397 (2016).

[Summary] Helices are ubiquitous in nature, and helical shape transition is often observed in residually stressed bodies, such as composites, wherein materials with different mechanical properties are glued firmly together to form a whole body. Inspired by a variety of biological examples, the basic physical mechanism responsible for the emergence of twisting and bending in such thin composite structures has been extensively studied. Here, we propose a simplified analytical model wherein a slender membrane tube undergoes a helical transition driven by the contraction of an elastic ribbon bound to the membrane surface. We analytically predict the curvature and twist of an emergent helix as functions of differential strains and elastic moduli, which are confirmed by our numerical simulations. Our results may help understand shapes observed in different biological systems, such as spiral bacteria, and could be applied to novel designs of soft machines and robots.