Air-encapsulating elastic mechanism of submerged Taraxacum blowballs.

In this article, we report the observation of an air-encapsulating elastic mechanism of Dandelion spherical seed heads, namely blowballs, when submerged underwater. This peculiarity seems to be fortuitous since Taraxacum is living outside water; nevertheless, it could become beneficial for a better survival under critical conditions, e.g. of temporary flooding. The scaling of the volume of the air entrapped suggests its fractal nature with a dimension of 2.782 and a fractal air volume fraction of 4.82 × 10-2 m0.218, resulting in nominal air volume fractions in the range of 14-23%. This aspect is essential for the optimal design of bioinspired materials made up of Dandelion-like components. The miniaturization of such components leads to an increase in the efficiency of the air encapsulation up to the threshold (efficiency = 1) achieved for an optimal critical size. Thus, the optimal design is accomplished using small elements, with the optimal size, rather than using larger elements in a lower number. The described phenomenon, interesting per se, also brings bioinspired insights toward new related technological solutions for underwater air-trapping and air-bubbles transportation, e.g. the body surface of a man could allow an apnea (air consumption of 5-10 l/min) of about 10 min if it is covered by a material made up of a periodic repetition of Dandelion components of diameter ≅ 18 µm and having a total thickness of about 3-6 cm.

Ceramics with the signature of wood: a mechanical insight.

In an attempt to mimic the outstanding mechanical properties of wood and bone, a 3D heterogeneous chemistry approach has been used in a biomorphic transformation process (in which sintering is avoided) to fabricate ceramics from rattan wood, preserving its hierarchical fibrous microstructure. The resulting material (called biomorphic apatite â€‹[BA] henceforth) possesses a highly bioactive composition and is characterised by a multiscale hierarchical pore structure, based on nanotwinned hydroxyapatite lamellae, which is shown to display a lacunar fractal nature. The mechanical properties of BA are found to be exceptional (when compared with usual porous hydroxyapatite and other ceramics obtained from wood through sintering) and unique â€‹as they occupy a zone in the Ashby map previously free from ceramics, but not far from wood and bone. Mechanical tests show the following: (i) the strength in tension may exceed that in compression, (ii) failure in compression involves complex exfoliation patterns, thus resulting in high toughness, (iii) unlike in sintered porous hydroxyapatite, fracture does not occur 'instantaneously,' â€‹but its growth may be observed, and it exhibits tortuous patterns that follow the original fibrillar structure of wood, thus yielding outstanding toughness, (iv) the anisotropy of the elastic stiffness and strength show unprecedented values when situations of stresses parallel and orthogonal to the main channels are compared. Despite being a ceramic material, BA displays a mechanical behavior similar on the one hand to the ligneous material from which it was produced (therefore behaving as a 'ceramic with the signature of wood') and on the other hand to the cortical/spongy osseous complex constituting the structure of compact bone.

Omnidirectional flexural invisibility of multiple interacting voids in vibrating elastic plates.

In elasticity, the design of a cloaking for an inclusion or a void to leave a vibrational field unperturbed by its presence, so to achieve its invisibility, is a thoroughly analysed, but still unchallenged, mechanical problem. The 'cloaking transformation' concept, originally developed in electromagnetism and optics, is not directly applicable to elastic waves, displaying a complex vectorial nature. Consequently, all examples of elastic cloaking presented so far involve complex design and thick coating skins. These cloakings often work only for problems of unidirectional propagation, within narrow ranges of frequency, and considering only one cloaked object. Here, a new method based on the concept of reinforcement, achieved via elastic stiffening and mass redistribution, is introduced to cloak multiple voids in an elastic plate. This simple technique produces invisibility of the voids to flexural waves within an extremely broad range of frequencies and thus surpassing in many aspects all existing cloaking techniques. The proposed design principle is applicable in mechanical problems ranging from the micro-scale to the scale of civil engineering. For instance, our results show how to design a perforated load-bearing building wall, vibrating during an earthquake exactly as the same wall, but unperforated, a new finding for seismic protection.

Serpentine locomotion through elastic energy release.

A model for serpentine locomotion is derived from a novel perspective based on concepts from configurational mechanics. The motion is realized through the release of the elastic energy of a deformable rod, sliding inside a frictionless channel, which represents a snake moving against lateral restraints. A new formulation is presented, correcting previous results and including situations never analysed so far, as in the cases when the serpent's body lies only partially inside the restraining channel or when the body has a muscle relaxation localized in a small zone. Micromechanical considerations show that propulsion is the result of reactions tangential to the frictionless constraint and acting on the snake's body, a counter-intuitive feature in mechanics. It is also experimentally demonstrated that the propulsive force driving serpentine motion can be directly measured on a designed apparatus in which flexible bars sweep a frictionless channel. Experiments fully confirm the theoretical modelling, so that the presented results open the way to exploration of effects, such as variability in the bending stiffness or channel geometry or friction, on the propulsive force of snake models made up of elastic rods.

From the elastica compass to the elastica catapult: an essay on the mechanics of soft robot arm.

An elastic rod is clamped at one end and has a dead load attached to the other (free) end. The rod is then slowly rotated using the clamp. When the load is smaller than the buckling value, the rod describes a continuous set of quasi-static forms and its end traces a (smooth, convex and simple) closed curve, which would be a circle if the rod were rigid. The closed curve is analytically determined through the integration of the Euler's elastica, so that for sufficiently small loads the mechanical system behaves as an 'elastica compass'. For loads higher than that of buckling, the elastica reaches a configuration from which a snap-back instability occurs, realizing a sort of 'elastica catapult'. The whole quasi-static evolution leading to the critical configuration for snapping is calculated through the elastica and the subsequent dynamic motion simulated using two numerical procedures, one ad hoc developed and another based on a finite-element scheme. The theoretical results are then validated on a specially designed and built apparatus. An obvious application of the present model would be in the development of soft robotic limbs, but the results are also of interest for the optimization analysis in pole vaulting.

Publisher's Note: Asymptotic self-restabilization of a continuous elastic structure [Phys. Rev. E 94, 063005 (2016)].

This corrects the article DOI: 10.1103/PhysRevE.94.063005.

Cymatics for the cloaking of flexural vibrations in a structured plate.

Based on rigorous theoretical findings, we present a proof-of-concept design for a structured square cloak enclosing a void in an elastic lattice. We implement high-precision fabrication and experimental testing of an elastic invisibility cloak for flexural waves in a mechanical lattice. This is accompanied by verifications and numerical modelling performed through finite element simulations. The primary advantage of our square lattice cloak, over other designs, is the straightforward implementation and the ease of construction. The elastic lattice cloak, implemented experimentally, shows high efficiency.

Asymptotic self-restabilization of a continuous elastic structure.

A challenge in soft robotics and soft actuation is the determination of an elastic system that spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behavior is that a displacement component spontaneously cycles around a null value, thus producing a cyclic soft mechanism. An example of such a system is theoretically proven through the solution of the elastica and a stability analysis based on dynamic perturbations. It is shown that the asymptotic self-restabilization is driven by the development of a configurational force, of similar nature to the Peach-Koehler interaction between dislocations in crystals, which is derived from the principle of least action. A proof-of-concept prototype of the discovered elastic system is designed, realized, and tested, showing that this innovative behavior can be obtained in a real mechanical apparatus.

Self-encapsulation, or the 'dripping' of an elastic rod.

A rod covering a fixed span is loaded at the middle with a transverse force, such that with increasing load a progressive deflection occurs. After a certain initial deflection, a phenomenon is observed where two points of the rod come in contact with each other. This is defined as the 'dripping point' and is when 'self-encapsulation' of the elastic rod occurs. Dripping seems at a first glance to be impossible and definitely cannot occur in the presence of 'ordinary' constraints (such as simple supports or clamps) at the ends of the span. However, the elastica governs oscillating pendulums, buckling rods and pendant drops, so that a possibility for self-encapsulation might be imagined. This phenomenon is indeed demonstrated (both theoretically and experimentally) to occur when at least one of the constraints at the ends of the rod is a sliding sleeve. This mechanical device generates a configurational force, causing the dripping of the rod, in a fully elastic set-up.

Torsional locomotion.

One edge of an elastic rod is inserted into a friction-less and fitting socket head, whereas the other edge is subjected to a torque, generating a uniform twisting moment. It is theoretically shown and experimentally proved that, although perfectly smooth, the constraint realizes an expulsive axial force on the elastic rod, which amount is independent of the shape of the socket head. The axial force explains why screwdrivers at high torque have the tendency to disengage from screw heads and demonstrates torsional locomotion along a perfectly smooth channel. This new type of locomotion finds direct evidence in the realization of a 'torsional gun', capable of transforming torque into propulsive force.

An elastica arm scale.

The concept of a 'deformable arm scale' (completely different from a traditional rigid arm balance) is theoretically introduced and experimentally validated. The idea is not intuitive, but is the result of nonlinear equilibrium kinematics of rods inducing configurational forces, so that deflection of the arms becomes necessary for equilibrium, which would be impossible for a rigid system. In particular, the rigid arms of usual scales are replaced by a flexible elastic lamina, free to slide in a frictionless and inclined sliding sleeve, which can reach a unique equilibrium configuration when two vertical dead loads are applied. Prototypes designed to demonstrate the feasibility of the system show a high accuracy in the measurement of load within a certain range of use. Finally, we show that the presented results are strongly related to snaking of confined beams, with implications for locomotion of serpents, plumbing and smart oil drilling.