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Register a new userEmploying pre-stress to generate finite cloaks for antiplane elastic waves
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It is shown that nonlinear elastic pre-stress of neo-Hookean hyperelastic materials can be used as a mechanism to generate finite cloaks and thus render objects near-invisible to incoming antiplane elastic waves. This approach appears to negate the requirement for special cloaking metamaterials with inhomogeneous and anisotropic material properties in this case. These properties are induced naturally by virtue of the pre-stress. This appears to provide a mechanism for broadband cloaking since dispersive effects due to metamaterial microstructure will not arise.
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A theory is presented showing that cloaking of objects from antiplane elastic waves can be achieved by elastic pre-stress of a neo-Hookean nonlinear elastic material. This approach would appear to eliminate the requirement of metamaterials with inhomogeneous anisotropic shear moduli and density. Waves in the pre-stressed medium are bent around the cloaked region by inducing inhomogeneous stress fields via pre-stress. The equation governing antiplane waves in the pre-stressed medium is equivalent to the antiplane equation in an unstressed medium with inhomogeneous and anisotropic shear modulus and isotropic scalar mass density. Note however that these properties are induced naturally by the pre-stress. Since the magnitude of pre-stress can be altered at will, this enables objects of varying size and shape to be cloaked by placing them inside the fluid-filled deformed cavity region.
An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically and is likely to describe the state of pre-stretch for a wide class of materials. A general class of strain-energy functions consistent with this assumption is derived. For this class of materials, the secular equation for incremental surface waves and the bifurcation condition for surface instability are shown to reduce to an equation involving only ordinary derivatives of the strain-energy equation. A compressible neo-Hookean material is considered as an example and it is found that finite compressibility has little quantitative effect on the speed of a surface wave and on the critical ratio of compression for surface instability.
A radial-dependent dispersive finite-difference time-domain (FDTD) method is proposed to simulate electromagnetic cloaking devices. The Drude dispersion model is applied to model the electromagnetic characteristics of the cloaking medium. Both lossless and lossy cloaking materials are examined and their operating bandwidth is also investigated. It is demonstrated that the perfect invisibility from electromagnetic cloaks is only available for lossless metamaterials and within an extremely narrow frequency band.
We examine several ways to manipulate the loss in electromagnetic cloaks, based on transformation electromagnetics. It is found that, by utilizing inherent electric and magnetic losses of metamaterials, perfect wave absorption can be achieved based on several popular designs of electromagnetic cloaks. A practical implementation of the absorber, consisting of ten discrete layers of metamaterials, is proposed. The new devices demonstrate super-absorptivity over a moderate wideband range, suitable for both microwave and optical applications. It is corroborated that the device is functional with a subwavelength thickness and, hence, advantageous compared to the conventional absorbers.
Experimental results and their interpretations are presented on the nonlinear acoustic effects of multiple scattered elastic waves in unconsolidated granular media. Short wave packets with a central frequency higher than the so-called cut-off frequency of the medium are emitted at one side of the statically stressed slab of glass beads and received at the other side after multiple scattering and nonlinear interactions. Typical signals are strongly distorted compared to their initially radiated shape both due to nonlinearity and scattering. It is shown that acoustic waves with a deformation amplitude much lower than the mean static deformation of the contacts in the medium can modify the elastic properties of the medium, especially for the weak contact skeleton part. This addresses the problem of reproducibility of granular structures during and after acoustic excitation, which is necessary to understand in the non destructive testing of the elastic properties of granular media by acoustic methods. Coda signal analysis is shown to be a powerful time-resolved tool to monitor slight modifications in the elastic response of an unconsolidated granular structure.
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