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

Endolithic colonization of fluid inclusion trails in mineral grains

Many scenarios for the colonization of planetary surfaces by microbial life involve endoliths. This study records microbial mass along fluid inclusion trails (healed microfractures) in quartz grains

Cadmium sulfide in a Mesoproterozoic terrestrial environment

Peer reviewedPostprin

Geochemistry and metallogeny of Neoproterozoic pyrite in oxic and anoxic sediments

The Neoproterozoic Dalradian Supergroup contains widespread diagenetic sulphides present as pyrite. The sulphides occur in both carbonaceous shales and glacial diamictites, that were deposited in relatively reducing and oxidising conditions respectively. The trace element compositions of the pyrite, and consequently the whole rock compositions, contrast between the two lithologies. The highest concentrations of selenium, tellurium and gold are all found in diamictite-hosted pyrite. The data suggest that increased mobility of these elements in oxidising conditions led to greater uptake when pyrite was precipitated. As one model for the formation of orogenic gold ore deposits assumes a sulphide-rich protolith, pyrite ultimately formed during relatively oxidising conditions could make a contribution, including the widespread pyrite precipitated during the Neoproterozoic ‘Snowball Earth’ glaciations

A black shale protolith for gold-tellurium mineralisation in the Dalradian Supergroup (Neoproterozoic) of Britain and Ireland

The Dalradian Supergroup of Britain and Ireland is mineralised by gold-tellurium vein deposits. The host succession includes carbonaceous, pyritic shales (pelites) which were a source of trace elements, including gold and tellurium. LA-ICP-MS mapping of pyrite crystals shows that late stages are enriched in gold, tellurium and lead, representing concentration of these elements during metamorphism and related hydrothermal activity. The sulphur isotope composition of the pyrite varies with stratigraphic position, reflecting an origin for the pyrite in the depositional environment through microbial sulphate reduction. Where pyrite was converted to pyrrhotite, trace element contents are much lower, indicating element liberation during metamorphism. These observations are consistent with a model of black shale protoliths for orogenic gold deposits