Session K14: Mechanical Metamaterials I

Metamaterials shake up textbook mechanics.

We defy two fundamental properties at the basis of mechanics using mechanical metamaterials close to topological transitions. First, we realize highly symmetric metamaterials whose stiffness is \textit{non-extensive}, namely it behaves non-monotonically as the system size is increased. Second, we create asymmetric and topological mechanical metamaterials that exhibit \textit{static non-reciprocity}, i.e. transmit displacements very differently when pushed from different sides. We further demonstrate that such non-extensive and non-reciprocal properties are associated with two distinct length scales that diverge when the metamaterials become isostatic and symmetric, respectively. These two limits, which correspond to two distinct topological transitions, provide a very efficient framework to largely enhance non-reciprocity and non-extensiveness and add significant design principles to the metamaterials toolbox.   

Designing functional materials with interfacial instabilities in thin films

We harness interfacial instabilities in thin liquid films to fabricate lens-shaped solid structures. A liquid elastomeric polymer is spin-coated on a flat substrate to create a uniform film, which is then turned upside-down, leading to the formation of a pattern of drops that emerges through the Rayleigh-Taylor instability. ~As the polymer cures, this array of liquid drops solidifies, thereby permanently structuring the geometry of the originally fluid system. The drops arrange in a lattice pattern with a wavelength that is well captured by stability analysis so that tuning the properties of the polymer enables us to tailor the morphology of the drops. Upon curing, the drops can then be peeled off from the substrate. Carefully designing a layout of surface defects, etched on the substrate onto which the thin film is initially deposited, is used as seed perturbations that trigger the instability in a controlled manner. This perturbation field significantly augments the monodispersity of the final solid structures, thereby making the fabrication process both robust and scalable. We demonstrate that by using an optically clear polymer (e.g. PDMS) during fabrication, the solid drops that are produced act as working lenses that can readily turn any smartphone into a microscope.   

Three dimensional Origami-based metamaterial

We present a novel cellular metamaterial constructed from Origami building blocks based on Miura-ori fold. The proposed cellular metamaterial exhibits unusual properties some of which stemming from the inherent properties of its Origami building blocks, and others manifesting due to its unique geometrical construction and architecture. These properties include foldability with two fully-folded configurations, auxeticity (i.e., negative Poisson's ratio), bistability, and self-locking of Origami building blocks to construct load-bearing cellular metamaterials. The kinematics and force response of the cellular metamaterial during folding were studied to investigate the underlying mechanisms resulting in its unique properties using analytical modeling and experiments.   

Auxetic metamaterials with additive manufacturing from jammed networks

Recent work has shown that the mechanical properties of disordered elastic networks can be precisely tuned to show a range of exotic properties. Starting from jammed configurations, we develop algorithms in simulation which modify the topology of these networks through bond pruning to create highly auxetic metamaterials which show promise in impact mitigation. Materials developed in simulation are produced in experiment, and the two show excellent agreement. We develop criteria which ensure that experimental realizations are highly tunable and maximize material resilience. We show that the Poisson's ratio can be further decreased by precisely tuning the mechanical strength of particular bonds in these networks. Interestingly, optimization algorithms show that ideal morphologies consist of a small fraction of highly rigid bonds, with the rest remaining more pliable. We employ additive manufacturing techniques to experimentally realize these heterogeneous materials.   

Spiral-based metamaterials: from local resonance to inertial amplification and Bragg scattering

Materials with engineered structural periodicity, obtained repeating in space unit cells with predetermined properties, can be used to modify the propagation of waves. In solids, such materials have been suggested for application in vibration insulation, acoustic focusing or elastic wave cloaking. Unit cells consisting of Archimedean spirals have rich dynamic properties and can be fabricated at the micro- and macro-scales, targeting different frequency ranges. Here, we show that by tuning the geometry of the spirals and arranging them in a lattice, they can act as Bragg scatterers, locally resonant metamaterials, or inertially amplified systems. We analyze the parametric transition between these three different band gap-opening mechanisms. We focus on the effect of inertial amplification and observe experimentally ultra-low and ultra-wide frequency bandgaps.   

Harnessing deformation to realize topological phase transition in acoustic metamaterials

We design a new class of acoustic metamaterials utilizing external force to realize topological phase transition. The proposed structure comprises a triangular array of steel cylinders coated by elastic rubbers in zigzag shape embodied in a water host. With numerical simulations, we show the topological phase of the band gap can pass from trivial to nontrivial when the shape of rubbers is axially compressed and a band inversion process occurs. The inherent link between the band inversion and the topological phase transition in the acoustic system of proposed structures is analogous to that in the electronic system of HgTe/CdTe quantum well structures. The helical edge states can exist along the interface between a topologically nontrivial acoustic metamaterial and a trivial one. Our work provides an easier way to realize topological phase transition in acoustic systems.   

Switchable topological phonon channels

Topological mechanical metamaterials offer a structured approach to create stable acoustic wave guides. The existence and stability of these wave guides is granted by the underlying topology, which typically allows to engineer arbitrarily shaped and backscattering free transport channels. However, due to their exceptional stability it can be tricky to terminate them or to temporarily shut them off without changing the material properties massively. I will discuss how one can take advantage of local symmetry breaking potentials to build a switchable topological phonon channel, and report on an experimental implementation of such a switch.   

Elastic multipole method for describing deformations of 2D solid structures

In recent years we have seen an explosion of mechanical metamaterials, where the geometry of highly deformable structures is responsible for their unusual properties, such as negative Poisson’s ratio, mechanical cloaking and tunable phononic band gaps. Understanding how such structures deform in response to applied external stresses is crucial for designing novel mechanical metamaterials. Here we present a method for predicting deformations of 2D solid structures with holes by employing analogies with electrostatics. Just like external electric field induces polarization (dipoles, quadrupoles, etc.) of conductive objects, external stress induces “elastic multipoles” inside holes. In structures with many holes the interactions between induced elastic multiploles are responsible for complex deformation patterns observed in experiments and finite element simulations. We demonstrate that our method can successfully predict deformation patterns in periodic as well as aperiodic structures with holes of varying sizes.   

Nonlinear modal enrichment in phononic crystals

Recent years have seen the advent of strategies to design metamaterials and phononic crystals with adaptive characteristics. Adaptivity is the ability of a system to autonomously modify its behavior in response to detected changes in the operating conditions. In this work we discuss the opportunities for the design of adaptive phononic crystals enabled by the exploitation of the nonlinearity embedded in the system. A well-known manifestation of nonlinearity is the generation of higher harmonics which, in complex dispersive systems, enables a rearrangement of the spectral response whereby part of the energy of an excited wave is deployed to a higher-frequency region of the band diagram, with the possibility to hop onto a different branch. The result is a mixture of modes with different (and possibly complementary) characteristics and an augmentation of the dynamic functionalities of the medium. In this work, we illustrate the versatility of this paradigm through a portfolio of lattice configurations. In these examples, mode hopping manifests either through the activation of new directional patterns in the wavefield, or through an enrichment of the wave modal content, for example by activating longitudinal components in wavefields originally dominated by shear mechanisms.   

Floppy Modes in Mechanical Metamaterials

We explore the rigidity for a model of hinged square tiles, which compose the backbone of a range of mechanical metamaterials. These non-generic systems allow for a single degree of freedom motion even for full filling, and here we explore the increase of the number of floppy modes when these systems are diluted (squares are removed). We discuss differences with rigidity percolation, due to the symmetric, non-generic nature of the building blocks.   

Anomalous acoustic dispersion in architected microlattice metamaterials

The ability to control dispersion in acoustic metamaterials is crucial to realize acoustic filtering and rectification devices as well as perfect imaging using negative refractive index materials. Architected microlattice metamaterials immersed in fluid constitute a versatile platform for achieving such control. We investigate architected microlattice materials able to exploit locally resonant modes of their fundamental building blocks that couple with propagating acoustic waves. Using analytical, numerical and experimental methods we find that such lattice materials show a hybrid dispersion behavior governed by Biot's theory for long wavelengths and multiple scattering theory when wave frequency is close to the resonances of the building block. We identify the relevant geometric parameters to alter and control the group and phase velocities in this class of acoustic metamaterials. Furthermore, we fabricate small-scale acoustic metamaterial samples using high precision SLA additive manufacturing and test the resulting materials experimentally using a customized ultrasonic setup. This work paves the way for new acoustic devices based on microlattice metamaterials.   

Mechanics of Simple Cubic Auxetic Microlattices

The mechanical properties of a polymeric simple cubic microlattice and its auxetic variations were investigated under quasi-static and shock loading. It was found that under quasi-static loading, an increasingly negative Poisson's ratio of the microlattices led to a decrease in lattice stiffness, as well as a shift from fracture dominated failure mode to bending dominated failure mode at large strain. Because of the change in failure mode, viscous dissipation initially increased as the lattices became more auxetic, but was eventually reduced due to the decreasing lattice stiffness. Similar observations were also made for the structures under shock loading, except that shock absorption through mechanical deformation of the lattices was always found to be higher for the auxetic lattices. This is mainly due to the effect of strain hardening and the fact that the auxetic microlattices were able to distribute stresses to the horizontal trusses even at high strain rates, unlike the case with the simple cubic design. Lastly, it was also found that scaling up the designs generally decreases the stiffness, viscous dissipation and shock absorption properties of the microlattices. The insights derived from this study are expected to be useful for designing the mechanical properties of materials of a given effective density.   

Buckling of a holey column

We report the results from a combined experimental and numerical investigation of buckling in a novel variant of an elastic column under axial load. We find that including a regular line of centred holes in the column can prevent conventional, global, lateral buckling. Instead, the local microstructure introduced by the holes allows the column to buckle in an entirely different, internal, mode in which the holes are compressed in alternate directions, but the column maintains the lateral reflection symmetry about its centreline. The internal buckling mode can be accommodated within a smaller external space than the global one; and it is the preferred buckling mode over an intermediate range of column lengths for sufficiently large holes. For very short or sufficiently long columns a modification of the classical, global, lateral buckling is dominant.