We study the crack propagation in a thin notched sheet of a polymeric material when two points in the sheet are pulled away. For materials of isotropic fracture energy, we show that an effective tearing vector predicting the direction of fracture propagation can be defined. In the flat sheet state, this vector is the perpendicular bisector of the vectors joining the pulling points and the fracture tip. The tearing vector is then differently oriented than the pulling direction. The "maximum energy released rate" criterion predicts a crack path that is tangential to the instantaneous tearing vector, or equivalently trajectories that are hyperbolas whose focal points are the pulling points. However, experiments indicate that fracture paths rarely follow this prediction because any small anisotropy existing in real thin sheets deviates the crack path from being parallel to the tearing vector. Although these deviations are locally small, as crack progresses a cumulative effect which results in large errors for long crack paths are observed. We therefore introduce the anisotropy effect through the generalization of the "maximum energy released rate" criterion and demonstrate that the crack trajectory and the minimum force to sustain tearing can be found through a Wulff's type geometrical construction. Systematic experiments show that the tearing force and fracture path are in good agreement with this prediction.
The physical mechanisms that bring about the propulsion of a rotating helix in a granular medium are considered. A propulsive motion along the axis of the rotating helix is induced by both symmetry breaking due to the helical shape, and the anisotropic frictional forces undergone by all segments of the helix in the medium. Helix dynamics is studied as a function of helix rotation speed and its geometrical parameters. The effect of the granular pressure and the applied external load were also investigated. A theoretical model is developed based on the anisotropic frictional force experienced by a slender body moving in a granular material, to account for the translation speed of the helix. A good agreement with experimental data is obtained, which allows for predicting the helix design to propel optimally within granular media. These results pave the way for the development of an efficient sand robot operating according to this mode of locomotion.
This study investigates the tearing of a thin notched sheet when two points on the sheet are pulled apart. The concepts that determine the crack trajectory are reviewed in the general anisotropic case, in which the energy of the fracture depends on the fracture direction. When observed as a flat sheet a purely geometric "tearing vector" is defined through the location of the crack tip and the pulling points. Both the Griffiths's criterion and the "maximum energy release rate criterion" (MERR) predict a fracture path that is parallel to the tearing vector in the isotropic case. However, for the anisotropic case, the application of the MERR leads to a crack path that deviates from the tearing vector, following a propagation direction that tends to minimize the fracture energy. In the case of strong anisotropy, it is more difficult to obtain an analytical prediction of the tearing trajectory. Thus, simple geometrical arguments are provided to give a derivation of a differential equation accounting for crack trajectory, according to the natural coordinates of the pulling, and in the case that the anisotropy is sufficiently weak. The solution derived from this analysis is in good agreement with previous experimental observations.
Non-cohesive materials such as sand, dry snow or cereals are encountered in various common circumstances, from everyday situations to industry. The process of digging into these materials remains a challenge to most animals and machines. Within the animal kingdom, different strategies are employed to overcome this issue, including excavation methods used by ants, the two-anchor strategy employed by soft burrowers such as razor-clams, and undulatory motions exhibited by sandfish lizards. Despite the development of technology to mimic these techniques in diggers and robots, the limitations of animals and machines may differ, and mimicry of natural processes is not necessarily the most efficient technological strategy. This study presents evidence that the resisting force for the penetration of an intruder into a dry granular media can be reduced by one order of magnitude with small amplitude (A ≃ 10 μm) and low frequency (f = 50 − 200 Hz) mechanical vibrations. This observed result is attributed to the local fluidization of the granular bed which induces the rupture of force chains. The drop in resistive force on entering dry granular materials may be relevant in technological development in order to increase the efficiency of diggers and robots.
This study investigates theoretically and numerically the propulsive sliding of a slender body. The body sustains a transverse and propagative wave along its main axis, and undergoes anisotropic friction caused by its surface texture sliding on the floor. A model accounting for the anisotropy of frictional forces acting on the body is implemented. This describes the propulsive force and gives the optimal undulating parameters for efficient forward propulsion. The optimal wave characteristics are effectively compared to the undulating motion of a slithering snakes, as well as with the motion of sandfish lizards swimming through the sand. Furthermore, numerical simulations have indicated the existence of certain specialized segments along the body that are highly efficient for propulsion, explaining why snakes lift parts of their body while slithering. Finally, the inefficiency of slithering as a form of locomotion to ascend a slope is discussed.
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