Effective material parameter retrieval of anisotropic elastic metamaterials with inherent nonlocality

Abstract

In this paper, the scattering (S-) parameter retrieval method is presented specifically for anisotropic elastic metamaterials; so far, no retrieval has been accomplished when elastic metamaterials exhibit fully anisotropic behavior. Complex constitutive property and intrinsic scattering behavior of elastic metamaterials make their characterization far more complicated than that for acoustic and electromagnetic metamaterials. In particular, elastic metamaterials generally exhibit anisotropic scattering behavior due to higher scattering modes associated with shear deformation. They also exhibit nonlocal responses to some degrees, which originate from strong multiple scattering interactions even in the long wavelength limit. Accordingly, the conventional S-parameter retrieval methods cannot be directly used for elastic metamaterials, because they determine only the diagonal components in effective tensor property. Also, the conventional methods simply use the analytic inversion formulae for the material characterization so that inherent nonlocality cannot be taken into account. To establish a retrieval method applicable to anisotropic elastic metamaterials, we propose an alternative S-parameter method to deal with full anisotropy of elastic metamaterials. To retrieve the whole effective anisotropic parameter, we utilize not only normal but also oblique wave incidences. For the retrieval, we first retrieve the ratio of the effective stiffness tensor to effective density and then determine the effective density. The proposed retrieval method is validated by characterizing the effective material parameters of various types of non-resonant anisotropic metamaterials. It is found that the whole effective parameters are retrieved consistently regardless of used retrieval conditions in spite of inherent nonlocality.

Recent Advances in Non-Traditional Elastic Wave Manipulation by Macroscopic Artificial Structures

“…The other method is the S-parameter retrieval method (SPRM) that numerically extracts effective parameters through scattering components by a toy model. Notice that only a handful of studies on SPRM in EMTMs exists, and one can be found that effective mass density and stiffness have been investigated considering full anisotropy with intrinsic nonlocal responses in the system [54].…”

Overall constitutive description of symmetric layered media based on scattering of oblique SH waves

“…Having in mind the x 1 -symmetry of the system, which leads to κ 35 being an odd function of s 2 , the values of µ 55 and η 33 can be determined exactly from Equations (38), (39). However, the value of µ 54 will be a function of κ 35 as:…”

“…In these works, the focus has been on propagation of pressure acoustic waves and the effect of microstructure on effective bulk modulus and density. Lee et al [39], extended the work in [34] to mechanical metamaterials, where the elasticity tensor components, beyond just the bulk modulus, are incorporated. Recently a mathematically exact theory for Willis-type media has been developed along with a matching field integration technique for normal incidence in [40], where transfer matrix method (TMM) is used to calculate the scattering exactly.…”

Transmodal Fabry-Pérot Resonance: Theory and Realization with Elastic Metamaterials

“…4(a)]. The void slits must be tilted at a certain angle with respect to the wave incidence direction for nonzero C 16 values [26]. The weakly and strongly coupled EMM layers consist of unit cells with 8 and 6 periods, respectively.…”

“…Fully detailed microstructures were considered for the finite element simulation [16]. The S-parameter method [26] was used to retrieve the C ij of the EMMs, which were used to calculate f theory . The theoretical TFPR frequency f theory predicted by Eq.…”