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Journal Club Theme of April 2013: Mechanical Metamaterials
Discussion on metamaterials (particularly dynamics of phononic/acoustic metamaterials) was first initiated in Journal Club Dec. 2007 (by Dr. Banerjee) and then recently again in Journal Clubs May 2012 (by Dr. Spadoni), June 2012 (by Dr. Kochmann) and Dec. 2012 (by Dr. Ruzzene). For the last five years, the research area in mechanical metamaterials has broadened so much that it now covers various unconventional macroscopic characteristics, not only dynamic properties (e.g., band-gaps, dynamic modulus/density, etc.) but also static properties (e.g., negative modulus, ultra-low density, etc.).
For the recent development in this area, I would recommend a review paper by Lee et al. . The paper summarizes several extraordinary mechanical characteristics and their fabrication techniques that have been recently reported. Unconventional functionalities can be classified into linear properties (e.g., elastic modulus-density, phononic band-gaps, Poisson’s ratio) and non-linear properties (e.g., specific energy absorption, high-strain-rate resistance). In this Journal Club, I would like to introduce a couple of related (and interesting!) topics which are not intensively covered in the review paper .
The so-called “extremal materials” are mechanical metamaterials characterized by the unconventional linear elastic properties. They were introduced by Milton and Cherkaev , and they are roughly defined as “materials for which the eigenvalues of the effective (elasticity) tensor only take (very) large or (very) small values.” The eigenmode corresponding to the very small eigenvalue is an easy mode of deformation, so the concept of nullmode, unimode, bimode, trimode, quadramode, and pentamode materials are introduced in 3-D elasticity. Using this terminology, an auxetic material having Poisson’s ratio of -1 can be viewed as a unimode material since it has substantially lower resistance for dilation than for shear deformations. So, the pentamode materials can only support a single type of stress component, and authors suggested that materials with arbitrary elasticity tensor can be developed using pentamode materials. Milton has recently published a series of papers on the characterization of these extremal materials [3, 4]. Moreover, the research group led by Wegener recently fabricated an “approximate” version of the conceptual pentamode material having negligible shear modulus . In this line of research, lots of interesting results can be produced from these unconventional extremal materials in the future.
For the metamaterials characterized by their unconventional non-linear properties, it is worthwhile to mention materials having tunable properties though non-affine (i.e., non-homogeneous) transformation. In the recent paper by Li et al. , dramatic color-switching is achieved through non-affine mechanical pattern transformation in shape memory polymer (SMP). When membranes having hexagonal arrangement of micron-size circular holes were hot-pressed, the circular holes deformed to ellipses and eventually closed resulting in featureless surface of membranes (Fig1.A). During this procedure, thus the initial membranes with diffraction color become a transparent film. An extended version of this 2-D non-affine transformation to 3-D spherical shells was also reported by Shim et al. . They introduce a class of continuum spherical shell structures patterned with a uniform arrangement of circular holes, and those structures undergo non-affine transformation induced by buckling under pressure, resulting in isotropic volume reduction (Fig1.B). Thanks to this unconventional feature, the proposed spherical structures can be used as building blocks to construct 3-D symmetric auxetic metamaterials.
Currently, investigation of phononic/acoustic metamaterials is mostly limited to small amplitudes of deformation, thus leading to linear analysis. In the future, nonlinear wave propagation analysis considering large deformation (particularly though non-affine transformation) could provide ample opportunity for practical applications (e.g. extreme loading conditions).
Fig. 1 (A) Top: Optical images of the original and deformed shape memory polymer (SMP) membranes on top of the “Penn” log. Bottom: Numerical simulation results for the SMP thermo-mechanical cycle. (B) The complete set of spherical shells patterned with uniform distribution of circular holes, leading to buckling-induced isotropic volume reduction.
 J.-H. Lee, J.P. Singer and E.L. Thomas (2012) Micro-/Nanostructred mechanical metamaterials , Advanced Materials, 24:4782.
 G.W. Milton and A.V. Cherkaev (1995) Which elasticity tensors are realizable? , Journal of Engineering Materials and Technology, 117:483.
 G.W. Milton (2012) Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots, Journal of Mechanics and Physics of Solids, http://dx.doi/org/10.1016/j.jmps.2012.08.011
 G.W. Milton (2012) Adaptable nonlinear bimode metamaterials using rigid bars, pivots, and actuators, Journal of Mechanics and Physics of Solids, http://dx.doi/org/10.1016/j.jmps.2012.08.012
 M. Kadic, T. Buckmann, N. Stenger, M. Thiel and M. Wegener (2012) On the practicability of pentamode mechanical metamaterials, Applied Physics Letters, 100:191901.
 J. Li, J. Shim, J. Deng, J.T.B. Overvelde, X. Zhu, K. Bertoldi and S. Yang (2012) Switching photonic membranes via pattern transformation and shape memory effect , Soft Matter, 8:10322.
 J. Shim, C. Perdigou, E.R. Chen, K. Bertoldi, P.M. Reis (2012) Buckling-induced encapsulation of structured elastic shells under pressure , Proceedings of the National Academy of Sciences of the USA, 109:5978.