Nonlinear pre-stress for cloaking from antiplane elastic waves

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.Comment: 21 pages, 4 figure

The Hill and Eshelby tensors for ellipsoidal inhomogeneities in the Newtonian potential problem and linear elastostatics

In 1957 Eshelby showed that a homogeneous isotropic ellipsoidal inhomogeneity embedded in a homogeneous isotropic host would feel uniform strains and stresses when uniform strains or stresses are applied in the far-field. Of specific importance is the uniformity of Eshelby's tensor S. Following this paper a vast literature has been generated using and developing Eshelby's result and ideas, leading to some beautiful mathematics and extremely useful results in a wide range of application areas. In 1961 Eshelby conjectured that for anisotropic materials only ellipsoidal inhomogeneities would lead to such uniform interior fields. Although much progress has been made since then, the quest to prove this conjecture is still not complete; numerous important problems remain open. Following a different approach to that considered by Eshelby, a closely related tensor P=S D^0 arises, where D^0 is the host medium compliance tensor. The tensor P is associated with Hill and is of course also uniform when ellipsoidal inhomogeneities are embedded in a homogeneous host phase. Two of the most fundamental and useful areas of applications of these tensors are in Newtonian potential problems such as heat conduction, electrostatics, etc. and in the vector problems of elastostatics. Micromechanical methods established mainly over the last half-century have enabled bounds on and predictions of the effective properties of composite media. In many cases such predictions can be explicitly written down in terms of the Hill, or equivalently the Eshelby tensor and can be shown to provide excellent predictions in many cases. Here this classical problem is revisited and a large number of results for problems that are felt to be of great utility in a wide range of disciplines are derived or recalled

Band Gap Formation and Tunability in Stretchable Serpentine Interconnects

Serpentine interconnects are highly stretchable and frequently used in flexible electronic systems. In this work, we show that the undulating geometry of the serpentine interconnects will generate phononic band gaps to manipulate elastic wave propagation. The interesting effect of `bands-sticking-together' is observed. We further illustrate that the band structures of the serpentine interconnects can be tuned by applying pre-stretch deformation. The discovery offers a way to design stretchable and tunable phononic crystals by using metallic interconnects instead of the conventional design with soft rubbers and unfavorable damping.Comment: 12 pages, 8 figure

Hyperelastic antiplane ground cloaking

Hyperelastic materials possess the appealing property that they may be employed as elastic wave manipulation devices and cloaks by imposing pre-deformation. They provide an alternative to microstructured metamaterials and can be used in a reconfigurable manner. Previous studies indicate that exact elastodynamic invariance to pre-deformation holds only for neo-Hookean solids in the antiplane wave scenario and the semi-linear material in the in-plane compressional/shear wave context. Furthermore, although ground cloaks have been considered in the acoustic context they have not yet been discussed for elastodynamics, either by employing microstructured cloaks or hyperelastic cloaks. This work therefore aims at exploring the possibility of employing a range of hyperelastic materials for use as antiplane ground cloaks (AGCs). The use of the popular incompressible Arruda-Boyce and Mooney-Rivlin nonlinear materials is explored. The scattering problem associated with the AGC is simulated via finite element analysis where the cloaked region is formed by an indentation of the surface. Results demonstrate that the neo-Hookean medium can be used to generate a perfect hyperelastic AGC as should be expected. Furthermore, although the AGC performance of the Mooney-Rivlin material is not particularly satisfactory, it is shown that the Arruda-Boyce medium is an excellent candidate material for this purpose

Acoustic scattering from a strained region

A composite material consists of a rubber filled with gas-filled microspheres. In underwater applications it is compressed hydrostatically by a pressure that may be not insignificant compared with the shear modulus of the rubber, so large strains are produced around each spherical inclusion. When these spherical inclusions scatter an incident acoustic wave, the strained region around an inclusion has had its elastic properties altered by the large static strain. Thales Underwater Systems asked the Study Group to address the question of how this strained region affects the elastic scattering, bearing in mind that the dynamic shear modulus differs from its static value

Loss Compensation in Time-Dependent Elastic Metamaterials

Materials with properties that are modulated in time are known to display wave phenomena showing energy increasing with time, with the rate mediated by the modulation. Until now there has been no accounting for material dissipation, which clearly counteracts energy growth. This paper provides an exact expression for the amplitude of elastic or acoustic waves propagating in lossy materials with properties that are periodically modulated in time. It is found that these materials can support a special propagation regime in which waves travel at constant amplitude, with temporal modulation compensating for the normal energy dissipation. We derive a general condition under which amplification due to time-dependent properties offsets the material dissipation. This identity relates band-gap properties associated with the temporal modulation and the average of the viscosity coefficient, thereby providing a simple recipe for the design of loss-compensated mechanical metamaterials

Image of the Teacher in Educational Leadership

Is the early childhood teacher a babysitter and the banker of knowledge lling empty-headed children with meaningless information? Or, is the teacher of young children a facilitator, guide and co-learner at the round-table of learning with competent children and educational community participants? Ex- amining teaching and learning, organizational leadership, politics and policy, and educational research, this paper explores the image of the teacher as a theoretical discussion in educational leadership with a fundamental question: How can teaching and learning, organizational leadership, politics and policy, and educational research inform and bolster the image of the early childhood teacher? Solutions are suggested to combat teacher image problems which include utilizing a constructivist paradigm; engaging parents, teachers, sta , and community to collaborate on the subject of teacher image and classroom learning practices; adopting the teacher, parent and child\u27s voice in the political arena; and, supporting teachers as researchers through documentation, collaboration, re ection and narration

Studies on the Scottish Mountain Blackfaced sheep: with special reference to the inheritance of certain breed characteristics

GENERAI,: Available evidence seems to show that the Scottish Blackface breed is not an indigenous breed of sheep in Scotland. It has been introduced from the south and has spread northwards. The breed has never become successfully established in Caithness and Sutherland: otherwise it has become the most numerous and important breed in the remaining mountain- ous parts of the country. It is probable that its characters have been influenced by crossing with the native "dun" - or with the. "white-faced" sheep and the infusion of this and possibly other blood may explain in part the differing characters in various districts. FLEECE CHARACTERS: The character of the fleece varies in diftferent districts in Scotland: so much so that definite areas are associated with the production of various grades of Blackface wool required for tweeds, carpets mattresses and so on. The reasons for the difference between the fleeces of these districts are not obvious it is suggested however that there may be some areas where a larger amount of unimproved blood enters into the compositon of the sheep stocks than elsewhere and that parasitic infestation and variation in the mineral and other content of the pasture may collectively or individually play a large part in this differentiation. Climatic conditions per se do not appear to exert that considerable influence on fleece which is usually attributed to them. CROSSING: The results of crossing with modern breeds of sheep has been considered and it seems evident that some of the characters are sex -linked, (for example the fleece characters of the Blackface x Gritstone.) Of the other crosses that with the Merino appears to be of the greatest interest, since increased density of fleece could still be demonstrated in the fourth generation of back- crossing to the Blackface. In practically all crosses rams of other breeds have been crossed with Blackface ewes. Crossing with Border Leicesters and Wensleydale are important commercial crosses, producing sheep, specially useful for the butcher. FACE COLOUR: The relationship between face-colour and various other factors has been considered, mainly from data accumulated on the writer's own farm in Perthshire during the past ten years. These results indicate that breeders can, by selection of their stock, with due regard to face colour, improve commercially important points. Sufficient data has been collected to show that by selection of the parents for face colours, a considerable proportion of the progeny will have those colours which this work has shown to be desirable, i.e. the extremes of face colour both black and white in ewes have been shown to be associated with lambs of inferior size and dead weights. That the face colour of the sire is important because it is shown that different colours are c-o,rrelat.ed with different decrees of hardiness in his lambs. It has been demonstrated that blackspotting in the fleece can be materially improved by using sires free from this fault and that black spotting and face colour are correlated. FERTILITY. It is shown that under a constant environment bath high and low fertility is transmitted from the sire to his daughters and is characteristically exhibited by thee: subsequently. It has not however been possible to test whether females may transmit fertility factors to their sons, and only very limited figures are given to show the influence of rams on their grand - daughters and on their sons, since only a few home -bred rams were used. Evidence is advanced which suggests potential economic importance of the influence of rams on the fertility of a Blackfaced breeding stock; for although the average for barrenness in this flock was 14%, one ram left daughters who were never barren, another ram's daughters only had a figure of 5% for barrenness, but four rams left daughters whose barrenness figures were 22 %, 23%, 24% and 29 %. FLOCK RECORDING: It is very evident that much valuable information on matters intimately concerned with breeding and inheritance under practical conditions is lost through the absence of a general system of marking and flock recording. The experience of marking and recording on which this work is based shows that the advantages gained compensate for the expenditure of such time and money as is involved