188 research outputs found
Elastodynamic cloaking and field enhancement for soft spheres
In this paper, we bring to the awareness of the scientific community and
civil engineers, an important fact: the possible lack of wave protection of
transformational elastic cloaks. To do so, we propose spherical cloaks
described by a non-singular asymmetric elasticity tensor depending upon a small
parameter that defines the softness of a region one would like to
conceal from elastodynamic waves. By varying , we generate a class of
soft spheres dressed by elastodynamic cloaks, which are shown to considerably
reduce the soft spheres' scattering. Importantly, such cloaks also provide some
wave protection except for a countable set of frequencies, for which some large
elastic field enhancement (resonance peaks) can be observed within the cloaked
soft spheres, hence entailing a possible lack of wave protection. We further
present an investigation of trapped modes in elasticity via which we supply a
good approximation of such Mie-type resonances by some transcendental equation.
Next, after a detailed presentation of spherical elastodynamic PML of Cosserat
type, we introduce a novel generation of cloaks, the mixed cloaks, as a
solution to the lack of wave protection in elastodynamic cloaking. Indeed,
mixed cloaks achieve both invisibility cloaking and protection throughout a
large range of frequencies. We think, mixed cloaks will soon be generalized to
other areas of physics and engineering and will in particular foster studies in
experiments.Comment: V2: major changes. More details on the study of trapped modes in
elasticity. Mixed cloaks introduced. Latex files, 27 pages, 14 figures. The
last version will appear at Journal of Physics D: Applied Physics.
Pacs:41.20.Jb,42.25.Bs,42.70.Qs,43.20.Bi,43.25.Gf. arXiv admin note: text
overlap with arXiv:1403.184
On near-cloaking for linear elasticity
We make precise some results on the cloaking of displacement fields in linear
elasticity. In the spirit of transformation media theory, the transformed
governing equations in Cosserat and Willis frameworks are shown to be
equivalent to certain high contrast small defect problems for the usual Navier
equations. We discuss near-cloaking for elasticity systems via a regularized
transform and perform numerical experiments to illustrate our near-cloaking
results. We also study the sharpness of the estimates from [H. Ammari, H. Kang,
K. Kim and H. Lee, J. Diff. Eq. 254, 4446-4464 (2013)], wherein the convergence
of the solutions to the transmission problems is investigated, when the Lam\'e
parameters in the inclusion tend to extreme values. Both soft and hard
inclusion limits are studied and we also touch upon the finite frequency case.
Finally, we propose an approximate isotropic cloak algorithm for a symmetrized
Cosserat cloak.Comment: 7 figures, 7 tables; Note that the earlier version of this preprint
was titled 'Some results in near-cloaking for elasticity systems'. This new
version of the manuscript has also seen some major upgrade. We have added a
new section on 'Cloaking parameters and isotropic approximation'. In there,
we propose an approximate isotropic cloak algorithm for a symmetrized
Cosserat cloa
Cloaking for a quasi-linear elliptic partial differential equation
In this article we consider cloaking for a quasi-linear elliptic partial
differential equation of divergence type defined on a bounded domain in
for . We show that a perfect cloak can be obtained via a
singular change of variables scheme and an approximate cloak can be achieved
via a regular change of variables scheme. These approximate cloaks though
non-degenerate are anisotropic. We also show, within the framework of
homogenization, that it is possible to get isotropic regular approximate
cloaks. This work generalizes to quasi-linear settings previous work on
cloaking in the context of Electrical Impedance Tomography for the conductivity
equation
Elastic scattering coefficients and enhancement of nearly elastic cloaking
The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic and electromagnetic media. In view of their promising applications, we introduce the notion of scattering coefficients of an elastic inclusion in this article. First, we define elastic scattering coefficients and substantiate that they naturally appear in the expansions of elastic scattered field and far field scattering amplitudes corresponding to a plane wave incidence. Then an algorithm is developed and analyzed for extracting the elastic scattering coefficients from multi-static response measurements of the scattered field. Moreover, the estimate of the maximal resolving order is provided in terms of the signal-to-noise ratio. The decay rate and symmetry of the elastic scattering coefficients are also discussed. Finally, we design scattering-coefficients-vanishing structures and elucidate their utility for enhancement of nearly elastic cloaking
Elastic scattering coefficients and enhancement of nearly elastic cloaking
The concept of scattering coefficients has played a pivotal role in a
broad range of inverse scattering and imaging problems in acoustic and
electromagnetic media. In view of their promising applications, we introduce
the notion of scattering coefficients of an elastic inclusion in this
article. First, we define elastic scattering coefficients and substantiate
that they naturally appear in the expansions of elastic scattered field and
far field scattering amplitudes corresponding to a plane wave incidence. Then
an algorithm is developed and analyzed for extracting the elastic scattering
coefficients from multi-static response measurements of the scattered field.
Moreover, the estimate of the maximal resolving order is provided in terms of
the signal-to-noise ratio. The decay rate and symmetry of the elastic
scattering coefficients are also discussed. Finally, we design
scattering-coefficients-vanishing structures and elucidate their utility for
enhancement of nearly elastic cloaking
Apparent negative values of Young’s moduli of lattice materials under dynamic conditions
Lattice materials are characterised by their equivalent elastic moduli for analysing mechanical properties of the microstructures. The values of the elastic moduli under static forcing condition are primarily dependent on the geometric properties of the constituent unit cell and the mechanical properties of the intrinsic material. Under a static forcing condition, the equivalent elastic moduli (such as Young’s modulus) are always positive. When dynamic forcing is considered, the equivalent elastic moduli become functions of the applied frequency and they can be negative at certain frequency values. This paper, for the first time, explicitly demonstrates the occurrence of negative equivalent Young’s modulus in lattice materials experimentally. Using additively manufactured titanium-alloy lattice metastructures, it is shown that the real part of experimentally measured in-plane Young’s modulus becomes negative under a dynamic environment. In fact, we show that the onset of such negative Young’s modulus in lattice materials can be precisely determined by capturing the sub-wavelength scale dynamics of the system. Experimental confirmation of the negative Young’s moduli and the onset of the same as a function of frequency provide the necessary physical insights and confidence for its potential exploitation in various multi-functional structural systems and devices across different length scales
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