On the practicability of pentamode mechanical metamaterials

Abstract

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...

On the Use of Mechanical Metamaterials for Innovative Seismic Isolations Systems

“…(7), with the numerical estimate of the same ratio given in Kadic et al [9], which has been obtained by fitting the results of finite element simulations of pentamode lattices under hydrostatic pressure and simple-shear loading Fig. 2 compares the predictions of Eqns.…”

“…This means that such a lattice material can be regarded as a "solid water" [3,8,9], which is well suited for the manufacturing of next generation seismic isolation devices. Table 1: Unit cells and elastic properties of three-dimensional lattice materials [11].…”

“…These may include: exceptional strength-and stiffness-to-weight ratios; excellent strain recoverability; very soft and/or very stiff deformation modes; auxetic behavior; phononic bandgaps; sound control ability; negative effective mass density; negative effective stiffness; negative effective refraction index; superlens behavior; and/or localized confined waves, to name some examples (cf. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein). The category of "extremal materials" has been introduced in [3] to define materials that simultaneously show very soft and very stiff deformation modes (unimode, bimode, trimode, quadramode and pentamode materials, depending on the number of soft modes).…”

“…-which feature special mechanical properties. Rapid prototyping techniques for the manufacture of materials with near-pentamode behavior have been recently presented in [8] (macroscale) and [9] (microscale). Pentamode materials have been proposed for transformation acoustics and elastomechanical cloak (refer, e.g., to the recent paper [10] and the references therein), but their potential in different engineering fields is still only partially explored.…”

“…The present study with the use of pentamode lattices as tunable seismic isolation devices, making profit from the control of the soft modes of such materials through the tuning of the bending moduli of members and junctions [8][9][10][11]. An illustrative numerical example shows a practical implementation of a pentamode lattice as a base isolation device, establishing a comparison of the elastic moduli and the force-displacement response of such a system with those exhibited by a conventional rubber bearing.…”