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 Poisson's ratio and with sufficient overall size for direct mechanical characterization aim at demonstrating the new possibilities with respect to rationally designed effective materials.

Conceptually, all conceivable three-dimensional mechanical materials can be built from pentamode materials. Pentamodes also enable to implement three-dimensional transformation acoustics -the analogue of transformation optics. However, pentamodes have not been realized experimentally to the best of our knowledge. Here, we investigate inasmuch the pentamode theoretical ideal suggested by Milton and Cherkaev in 1995 can be approximated by a metamaterial with current state-of-the-art lithography. Using numerical calculations calibrated by 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.Transformation optics can be seen as a design tool for steering light waves in a desired manner. In optics, one generally needs anisotropic magneto-dielectric (meta-) materials for, e.g., invisibility cloaks [1,2]. It is interesting to translate transformation optics to other types of waves such as acoustic waves. However, the three-dimensional elastodynamic equations are not invariant under coordinate transformations for scalar mass density and normal elastic materials [3]. In two dimensions or in thin plates, usual anisotropic elastic materials can suffice [4,5,6]. In three dimensions, one either needs materials with anisotropic mass density tensors [3,7,8,9] or pentamode materials [3,10,11,12] to implement the counterpart of invisibility cloaks or other devices. Neither of these materials has been realized experimentally so far.In 1995, Milton and Cherkaev [13] showed that all conceivable mechanical materials can be synthesized on the basis of pentamodes. Pentamodes are special in the sense that they avoid the coupling of compression and shear waves by making the bulk modulus, , extremely large compared to the shear modulus, , ideally infinitely large [13,14]. This situation corresponds to isotropic fluids, for which and thus the Poisson's ratio [15] is . Hence, pentamodes are sometimes also called "metafluids". Mathematically, ("penta") of the diagonal elements of the diagonalized elasticity tensor of an isotropic pentamode material are zero, and only one is non-zero [13,14].A conceptually perfect homogeneous pentamode material would literally immediately flow away. An intentionally spatially inhomogeneous pentamode structure would rapidly intermix and hence be destroyed, rendering these pentamode ideals essentially useless. Large metafluid viscosity could reduce these unwanted effects, but such internal friction would also introduce undesired damping/losses. Thus, in practice, one does want some finite shear modulus for stability. If the shear modulus is small compared to the bulk modulus, the ideas of transformation acoustics [3,7] are no longer exact, but are still expected to apply approximately. After all, perfect magneto-dielectrics have not been achieved in transformation optics either; nevertheless, striking results have been obtained with approximate materials [16,17].For reference, rega...

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.

Metamaterial-based cloaks make objects different from their surrounding appear just like their surrounding. To date, cloaking has been demonstrated experimentally in many fields of research, including electrodynamics at microwave frequencies, optics, static electric conduction, acoustics, fluid dynamics, thermodynamics and quasi two-dimensional solid mechanics. However, cloaking in the seemingly simple case of three-dimensional solid mechanics is more demanding. Here, inspired by invisible core-shell nanoparticles in optics, we design an approximate elasto-mechanical core-shell 'unfeelability' cloak based on pentamode metamaterials. The resulting three-dimensional polymer microstructures with macroscopic overall volume are fabricated by rapid dip-in direct laser writing optical lithography. We quasi-statically deform cloak and control samples in the linear regime and map the displacement fields by autocorrelation-based analysis of recorded movies. The measured and the calculated displacement fields show very good cloaking performance. This means that one can elastically hide objects along these lines.

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.