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Many works in elasticity have exploited the concept of gradient index (GRIN) lenses, borrowed from optics, for wave focusing and control. These effects are particularly attractive for cloaking, absorption or energy harvesting applications. Despite their potential, current lens designs suffer from limitations, mainly related to the difficulty in imaging point-like sources. Here, we exploit an alternative GRIN lens design, which enables a one-to-one correspondence between input and output phase, and allows to determine the focal length using the well-known thin lens equation, effectively establishing the elastic equivalent of the convex lens in optics. This is demonstrated analytically, obtaining a bijective relation between the location of a point-like source and its image, and the results are confirmed numerically and experimentally in an aluminium plate, where the lens is realized by introducing rows of circular cavities of variable diameters. Moreover, a proof-of-concept experiment demonstrates the possibility to image sources of flexural waves at the centimetre scale with subwavelength resolution. This research can extend applications of elastic GRIN lenses to new fields such as imaging and non-destructive testing, where the location of defects can be identified by focusing the scattered field. Multiple sources can be imaged simultaneously, and the combined effect of multiple lenses can also be used to design more complex systems, opening new possibilities in the technological exploitation of elastic wave manipulation.

Bioinspiration has widely been demonstrated to be a powerful approach for the design of innovative structures and devices. Recently, this concept has been extended to the field of elasticity, dynamics, and metamaterials. In this paper, we propose a seashell-inspired metasensor that can simultaneously perform spatial frequency mapping and act as a polarizer. The structure emerges from a universal parametric design that encompasses diverse spiral geometries with varying circular cross sections and curvature radii, all leading to tonotopic behavior. Adoption of an optimization process leads to a planar geometry that enables us to simultaneously achieve tonotopy for orthogonally polarized modes, leading to the possibility to control polarization as well as the spatial distribution of frequency maxima along the spiral axis. We demonstrate the versatility of the device and discuss the possible applications in the field of acoustics and sensing., Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in APL Mater. 12, 041104 (2024) and may be found at https://doi.org/10.1063/5.0201722

The extended plane wave expansion (EPWE) formulation is derived to obtain the complex band structure of flexural waves in viscoelastic thin phononic crystal plates considering the Kirchhoff-Love plate theory. The presented formulation yields the evanescent behavior of flexural waves in periodic thin plates considering viscoelastic effects. The viscosity is modeled by the standard linear solid model (SLSM), typically used to closely model the behavior of polymers. It is observed that the viscoelasticity influences significantly both the propagating and evanescent Bloch modes. The highest wave attenuation of the viscoelastic phononic thin plate is found around a unit cell filling fraction of 0.37 for higher frequencies considering the least attenuated wave mode. This EPWE formulation broadens the suitable methods to handle evanescent flexural waves in 2-D thin periodic plate systems considering the effects of viscoelasticity on wave attenuation.

In this paper, we discuss the possibility of achieving tunable topologically protected edge modes through the application of uniaxial deformation in an auxetic metamaterial. The proposed structure consists of a thin slab with oriented cuts in a hexagonal lattice, where topologically protected band gaps are opened by introducing a controlled variation in the cut lengths. Numerical simulations demonstrate the existence of topologically protected and scatter-free wave propagation in the structure at the interface between two sub-domains with modified cells, in distinct frequency ranges. This only occurs in the presence of auxeticity. In addition, exploiting geometrical nonlinearity, the application of a uniaxial strain can be used to close the topological band gaps or to modify their frequency range, i.e., to weaken the localization effects or to shift the frequency at which they occur. The spatial and temporal variation of the applied strain field can thus be used for the dynamic tuning of metamaterial topological waveguiding properties, with applications in mechanical devices for logic operations and computations., Comment: 37 pages, 12 figures

We propose a new conceptual approach to reach unattained dissipative properties based on the friction of slender concentric sliding columns. We begin by searching for the optimal topology in the simplest telescopic system of two concentric columns. Interestingly, we obtain that the optimal shape parameters are material independent and scale invariant. Based on a multiscale self-similar reconstruction, we end-up with a theoretical optimal fractal limit system whose cross section resembles the classical Sierpi\'nski triangle. Our optimal construction is finally completed by considering the possibility of a complete plane tessellation. The direct comparison of the dissipation per unit volume with the material dissipation up to the elastic limit shows a great advantage: . Such result is already attained for a realistic case of three only scales of refinement leading almost (96%) the same dissipation of the fractal limit. We also show the possibility of easy recovering of the original configuration after dissipation and we believe that our schematic system can have interesting reliable applications in different technological fields. Interestingly, our multiscale dissipative mechanism is reminiscent of similar strategies observed in nature as a result of bioadaptation such as in the archetypical cases of bone, nacre and spider silk. Even though other phenomena such as inelastic behavior and full tridimensional optimization are surely important in such biological systems, we believe that the suggested dissipation mechanism and scale invariance properties can give insight also in the hierarchical structures observed in important biological examples.

Marine shells are designed by nature to ensure mechanical protection from predators and shelter for mollusks living inside them. A large amount of work has been done to study the multiscale mechanical properties of their complex microstructure and to draw inspiration for the design of impact-resistant biomimetic materials. Less is known regarding the dynamic behavior related to their structure at multiple scales. Here, we present a combined experimental and numerical study of the shells of two different species of gastropod sea snail belonging to the Turritellidae family, featuring a peculiar helicoconic shape with hierarchical spiral elements. The proposed procedure involves the use of micro-Computed Tomography scans for the accurate determination of geometry, Atomic Force Microscopy and Nanoindentation to evaluate local mechanical properties, surface morphology and heterogeneity, as well as Resonant Ultrasound Spectroscopy coupled with Finite Element Analysis simulations to determine global modal behavior. Results indicate that the specific features of the considered shells, in particular their helicoconic and hierarchical structure, can also be linked to their vibration attenuation behavior. Moreover, the proposed investigation method can be extended to the study of other natural systems, to determine their structure-related dynamic properties, ultimately aiding the design of bioinspired metamaterials and of structures with advanced vibration control., Comment: 28 pages, 20 figures

Bone is a stiff and though, hierarchical and continuously evolving material that optimizes its structure to respond to mechanical stimuli, which also govern growth and remodeling processes. However, a full understanding of the underlying mechanisms responsible for the cooperation of bone toughness and biological functions, with important implications in bone ageing, osteoporosis and tissue repair, has yet to be achieved. In particular, how micro-damage nucleation, needed for tissue remodeling, does not evolve into catastrophic failure in such a stiff material, still remains a partial enigma, cement lines, interfaces and sacrificial elements alone not providing a definitive answer to the question. Here, we bring to light a novel stress-based bone toughening mechanism, calling into play the nearly-symmetrical, chiral and hierarchical architecture of the osteons, demonstrating that their arrangement simultaneously gives rise to stress states alternating in sign along the osteon radius and to localized stress amplifications, both in the tensile and compressive regimes. This unveils a previously unforeseen synergistic mechanism allowing micro-damage accumulation without propagating cracks, kindled by the contrast between crack-opening due to tensile hoop stresses and crack-stopping due to compressive stresses at the crack tips in adjacent lamellae, which seal the crack ends conferring toughness to bone well beyond that predicted by current models. Furthermore, shear stresses occur at the lamellar interfaces, contributing with fluid flow to mechanically stimulate the osteocytes and to amplify the bone signalling. These results, obtained through original exact elastic solutions and confirmed by both FE fracture analyses and experimental tests on 3D-printed osteon prototypes, contribute with another piece in the puzzle to making the rational biophysical picture of bone mechanobiology complete.

Nature has engineered complex designs to achieve advanced properties and functionalities through evolution, over millions of years. Many organisms have adapted to their living environment producing extremely efficient materials and structures exhibiting optimized mechanical, thermal, optical properties, which current technology is often unable to reproduce. These properties are often achieved using hierarchical structures spanning macro, meso, micro and nanoscales, widely observed in many natural materials like wood, bone, spider silk and sponges. Thus far, bioinspired approaches have been successful in identifying optimized structures in terms of quasi-static mechanical properties, such as strength, toughness, adhesion, but comparatively little work has been done as far as dynamic ones are concerned (e.g. vibration damping, noise insulation, sound amplification, etc.). In particular, relatively limited knowledge currently exists on how hierarchical structure can play a role in the optimization of natural structures, although concurrent length scales no doubt allow to address multiple frequency ranges. Here, we review the main work that has been done in the field of structural optimization for dynamic mechanical properties, highlighting some common traits and strategies in different biological systems. We also discuss the relevance to bioinspired materials, in particular in the field of phononic crystals and metamaterials, and the potential of exploiting natural designs for technological applications.