Stress-wave energy management through material anisotropy

Amirkhizi, Alireza V.; Tehranian, Aref; Nemat‐Nasser, Sia

doi:10.1016/j.wavemoti.2010.03.005

Cited by 38 publications

(25 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The key idea that enabled progress in those areas was the combination of coordinate transformations with coordinate-dependent, and often extremely exotic [5,[13][14][15], material properties. Transformation optics [3][4][5]11,16] and transformation acoustics [6-8] offer solutions to some inverse scattering problems [17] by reducing them to an elementary one-for example, scattering off a point object in free space.There is no reason why this conceptual approach cannot be used in other areas of physics [18], and, in fact, it has already been applied to conductive heat transfer [19], linear elastodynamics [5,8,[20][21][22][23][24], surface wave [25], and quantum-mechanical matter wave [26] dynamics. The fundamental requirement for the applicability of this concept is the presence of a medium with sufficiently flexible properties, which enables manipulation of the coefficients in the equations describing the dynamical process.…”

mentioning

confidence: 99%

“…There is no reason why this conceptual approach cannot be used in other areas of physics [18], and, in fact, it has already been applied to conductive heat transfer [19], linear elastodynamics [5,8,[20][21][22][23][24], surface wave [25], and quantum-mechanical matter wave [26] dynamics. The fundamental requirement for the applicability of this concept is the presence of a medium with sufficiently flexible properties, which enables manipulation of the coefficients in the equations describing the dynamical process.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Fluid Flow Control with Transformation Media

2011

View full text Add to dashboard Cite

We introduce a new concept for the manipulation of fluid flow around three-dimensional bodies. Inspired by transformation optics, the concept is based on a mathematical idea of coordinate transformations and physically implemented with anisotropic porous media permeable to the flow of fluids. In two situations-for an impermeable object placed either in a free-flowing fluid or in a fluid-filled porous medium-we show that the object can be coated with an inhomogeneous, anisotropic permeable medium, such as to preserve the flow that would have existed in the absence of the object. The proposed fluid flow cloak eliminates downstream wake and compensates viscous drag, hinting at the possibility of novel propulsion techniques. As a subset of the separation of variables method, conformal transformations thus offer a unique and powerful approach to the forward problems of incompressible flow, as well as electro-and magnetostatics.The utility of more general coordinate transformations in the inverse electromagnetic [3][4][5] and acoustic [6][7][8][9] problems has been demonstrated recently, most impressively by showing the possibility of electromagnetic invisibility, dubbed cloaking [3,4,[10][11][12]. The key idea that enabled progress in those areas was the combination of coordinate transformations with coordinate-dependent, and often extremely exotic [5,[13][14][15], material properties. Transformation optics [3][4][5]11,16] and transformation acoustics [6-8] offer solutions to some inverse scattering problems [17] by reducing them to an elementary one-for example, scattering off a point object in free space.There is no reason why this conceptual approach cannot be used in other areas of physics [18], and, in fact, it has already been applied to conductive heat transfer [19], linear elastodynamics [5,8,[20][21][22][23][24], surface wave [25], and quantum-mechanical matter wave [26] dynamics. The fundamental requirement for the applicability of this concept is the presence of a medium with sufficiently flexible properties, which enables manipulation of the coefficients in the equations describing the dynamical process. Here, we propose porous media as a substrate for transformation fluid dynamics and investigate the feasibility of controlling certain features of incompressible fluid flow.The electromagnetic cloak of invisibility, which inspired this approach, manipulates the field lines of electric and magnetic fields, and the streamlines of momentum flux, in such a manner that these lines are virtually indistinguishable from those in the absence of any object [3]. Because the streamlines are unperturbed in the free space outside the cloak, electromagnetic radiation avoids scattering off the structure and therefore exerts no electromagnetic pressure on it. Achieving a similar level of control over the streamlines of the fluid flow outside the structure would imply canceling the viscous drag exerted on the structure. In this Letter, we demonstrate the possibility of fluid flow cloaking using porous media whose properties...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Fluid Flow Control with Transformation Media

2011

View full text Add to dashboard Cite

show abstract

“…Norris [19] showed that Cosserat type materials [120] would also serve the purpose. Some other techniques which have been studied for elastic wave cloaking include using anisotropy [121] and nonlinear prestressing [122][123][124][125].…”

Section: Coordinate Transformations and Metamaterialsmentioning

confidence: 99%

Elastic metamaterials and dynamic homogenization: a review

Srivastava

2015

International Journal of Smart and Nano Materials

122

View full text Add to dashboard Cite

In this paper, we review the recent advances which have taken place in the understanding and applications of acoustic/elastic metamaterials. Metamaterials are artificially created composite materials which exhibit unusual properties that are not found in nature. We begin with presenting arguments from discrete systems which support the case for the existence of unusual material properties such as tensorial and/or negative density. The arguments are then extended to elastic continuums through coherent averaging principles. The resulting coupled and nonlocal homogenized relations, called the Willis relations, are presented as the natural description of inhomogeneous elastodynamics. They are specialized to Bloch waves propagating in periodic composites and we show that the Willis properties display the unusual behavior which is often required in metamaterial applications such as the Veselago lens. We finally present the recent advances in the area of transformation elastodynamics, charting its inspirations from transformation optics, clarifying its particular challenges, and identifying its connection with the constitutive relations of the Willis and the Cosserat types.

show abstract

“…Tsai [1]. Furthermore, such layered and FRC materials have the potential to be of great use in modern metamaterial applications as was described by Torrent and Sanchez-Dehesa [2] and Amirkhizi et al [3] for example. The main objective of this article is to pull together ideas relating to FRCs from a variety of diverse publications, placing particular emphasis on the explicit construction and computation of the Hashin-Shtrikman bounds on effective elastic constants, including information regarding the two-point correlation functions associated with the distribution of inclusion phases.…”

Section: Introductionmentioning

confidence: 99%

On the computation of the Hashin–Shtrikman bounds for transversely isotropic two-phase linear elastic fibre-reinforced composites

Parnell

Calvo‐Jurado

2015

J Eng Math

View full text Add to dashboard Cite

Although various forms for the Hashin-Shtrikman bounds on the effective elastic properties of inhomogeneous materials have been written down over the last few decades, it is often unclear how to construct and compute such bounds when the material is not of simple type (e.g. isotropic spheres inside an isotropic host phase). Here, we show how to construct, in a straightforward manner, the Hashin-Shtrikman bounds for generally transversely isotropic two-phase particulate composites where the inclusion phase is spheroidal, and its distribution is governed by spheroidal statistics. Note that this case covers a multitude of composites used in applications by taking various limits of the spheroid, including both layered media and long unidirectional composites. Of specific interest in this case is the fact that the corresponding Eshelby and Hill tensors can be derived analytically. That the shape of the inclusions and their distribution can be specified independently is of great utility in composite design. We exhibit the implementation of the computations with several examples.

show abstract

Stress-wave energy management through material anisotropy

Cited by 38 publications

References 19 publications

Fluid Flow Control with Transformation Media

Fluid Flow Control with Transformation Media

Elastic metamaterials and dynamic homogenization: a review

On the computation of the Hashin–Shtrikman bounds for transversely isotropic two-phase linear elastic fibre-reinforced composites

Contact Info

Product

Resources

About