Muamer Kadic

Tailored 3D Mechanical Metamaterials Made by Dip‐in Direct‐Laser‐Writing Optical Lithography

Dip-in direct-laser-writing (DLW) optical lithography allows fabricating complex three-dimensional microstructures without the height restrictions of regular DLW. Bow-tie elements assembled into mechanical metamaterials with positive/zero/negative Poissons ratio and with sufficient overall size for direct mechanical characterization aim at demonstrating the new possibilities with respect to rationally designed effective materials.

Experiments on Transformation Thermodynamics: Molding the Flow of Heat

It was recently shown theoretically that the time-dependent heat conduction equation is form invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped onto (meta)materials with spatially inhomogeneous and anisotropic heat-conductivity tensors in the laboratory space. On this basis, we design, fabricate, and characterize a microstructured thermal cloak that molds the flow of heat around an object in a metal plate. This allows for transient protection of the object from heating while maintaining the same downstream heat flow as without object and cloak.

On the practicability of pentamode mechanical metamaterials

Following the theoretical suggestion by Milton and Cherkaev in 1995, we fabricate pentamode metamaterials by dip-in direct-laser-writing optical lithography. Using finite element calculations and geometrical parameters corresponding to our fabricated three-dimensional microstructures, we find that the figure of merit, i.e., the ratio of bulk modulus to shear modulus, can realistically be made as large as about 1,000. This result opens new horizons for transformation acoustics.

Invisibility cloaking in a diffusive light scattering medium

To cast no shadow in a murky medium Cloaks can hide objects from view, but what about their shadows? Schittny et al. devised a cloak to remove even the shadow of an object embedded in a murky medium in front of a computer screen (see the Perspective by Smith). They engineered a core-shell structure within which an object could be hidden and tailored the optical properties of the cloak to match that of the medium. Light was routed around the cloak, leaving no trace of the hidden object. Science, this issue p. 427; see also p. 384 A core-shell structure provides a cloak for objects within a diffusive medium. [Also see Perspective by Smith] In vacuum, air, and other surroundings that support ballistic light propagation according to Maxwell’s equations, invisibility cloaks that are macroscopic, three-dimensional, broadband, passive, and that work for all directions and polarizations of light are not consistent with the laws of physics. We show that the situation is different for surroundings leading to multiple light scattering, according to Fick’s diffusion equation. We have fabricated cylindrical and spherical invisibility cloaks made of thin shells of polydimethylsiloxane doped with melamine-resin microparticles. The shells surround a diffusively reflecting hollow core, in which arbitrary objects can be hidden. We find good cloaking performance in a water-based diffusive surrounding throughout the entire visible spectrum and for all illumination conditions and incident polarizations of light.

On three-dimensional dilational elastic metamaterials

Dilational materials are stable, three-dimensional isotropic auxetics with an ultimate Poissonʼs ratio of −1. Inspired by previous theoretical work, we design a feasible blueprint for an artificial material, a metamaterial, which approaches the ideal of a dilational material. The main novelty of our work is that we also fabricate and characterize corresponding metamaterial samples. To reveal all modes in the design, we calculate the phonon band structures. On this basis, using cubic symmetry we can unambiguously retrieve all different non-zero elements of the rank-four effective metamaterial elasticity tensor from which all effective elastic metamaterial properties follow. While the elastic properties and the phase velocity remain anisotropic, the effective Poissonʼs ratio indeed becomes isotropic and approaches −1 in the limit of small internal connections. This finding is also supported by independent, static continuum-mechanics calculations. In static experiments on macroscopic polymer structures fabricated by three-dimensional printing, we measure Poissonʼs ratios as low as −0.8 in good agreement with the theory. Microscopic samples are also presented.

Three-dimensional labyrinthine acoustic metamaterials

Building upon recent theoretical and experimental work on two-dimensional labyrinthine acoustic metamaterials, we design, fabricate, and characterize nearly isotropic three-dimensional airborne acoustic labyrinthine metamaterials. Our experiments on aluminum-based structures show phase and group velocities smaller than that of air by a factor of about 8 over a broad range of frequencies from 1 to 4 kHz. This behavior is in agreement with three-dimensional band-structure calculations including the first and higher bands. The extracted imaginary parts of the phase velocity are 5–25 times smaller than the mentioned real parts. This ratio is better than for most optical metamaterials but still rather favors applications in terms of sub-wavelength broadband acoustic absorbers.

Tailored Buckling Microlattices as Reusable Light‐Weight Shock Absorbers

Structures and materials absorbing mechanical (shock) energy commonly exploit either viscoelasticity or destructive modifications. Based on a class of uniaxial light-weight geometrically nonlinear mechanical microlattices and using buckling of inner elements, either a sequence of snap-ins followed by irreversible hysteretic - yet repeatable - self-recovery or multistability is achieved, enabling programmable behavior. Proof-of-principle experiments on three-dimensional polymer microstructures are presented.

On anisotropic versions of three-dimensional pentamode metamaterials

Pentamode materials are artificial solids with elastic properties that approximate those of isotropic liquids. The corresponding three-dimensional mechanical metamaterials or ‘meta-liquids’ have recently been fabricated. In contrast to normal liquids, anisotropic meta-liquids are also possible—a prerequisite for realizing many of the envisioned transformation-elastodynamics architectures. Here, we study several possibilities theoretically for introducing intentional anisotropy into three-dimensional pentamode metamaterials. In static continuum mechanics, the transition from anti-auxetic pentamode materials to auxetics is possible. Near this transition, in the dynamic case, approximately uniaxial versions of pentamode metamaterials deliver anisotropic longitudinal-wave phase velocities different by nearly a factor of 10 for realistically accessible microstructure parameters.

Elastic measurements on macroscopic three-dimensional pentamode metamaterials

Pentamode metamaterials approximate tailorable artificial liquids. Recently, microscopic versions of these intricate three-dimensional structures have been fabricated, but direct experimental characterization has not been possible yet. Here, using three-dimensional printing, we fabricate macroscopic polymer-based samples with many different combinations of the small connection diameter d and the lattice constant a. Direct measurements of the static shear modulus and the Youngs modulus reveal that both scale approximately according to (d/a)3, in good agreement with continuum-mechanics calculations. For the smallest accessible values of d/a≈1.5%, we find derived ratios of bulk modulus B to shear modulus G of B/G≈1000.

Phonon band structures of three-dimensional pentamode metamaterials

Three-dimensional pentamode metamaterials are artificial solids that approximately behave like liquids, which have vanishing shear modulus. Pentamodes have recently become experimental reality. Here, we calculate their phonon band structures for various parameters. Consistent with static continuum mechanics, we find that compression and shear waves exhibit phase velocities that can realistically be different by more than one order of magnitude. Interestingly, we also find frequency intervals with more than two octaves bandwidth in which pure single-mode behavior is obtained. Herein, exclusively compression waves exist due to a complete three-dimensional band gap for shear waves and, hence, no coupling to shear modes is possible. Such single-mode behavior might, e.g., be interesting for transformation-elastodynamics architectures.