203 research outputs found
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
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
On nonlinear viscoelastic deformations - a reappraisal of Fung's quasilinear viscoelastic model
This article offers a reappraisal of Fung's method for quasilinear
viscoelasticity. It is shown that a number of negative features exhibited in
other works, commonly attributed to the Fung approach, are merely a consequence
of the way it has been applied. The approach outlined herein is shown to yield
improved behaviour, and offers a straightforward scheme for solving a wide
range of models. Results from the new model are contrasted with those in the
literature for the case of uniaxial elongation of a bar: for an imposed stretch
of an incompressible bar, and for an imposed load. In the last case, a
numerical solution to a Volterra integral equation is required to obtain the
results. This is achieved by a high order discretisation scheme. Finally, the
stretch of a compressible viscoelastic bar is determined for two distinct
materials: Horgan-Murphy and Gent
Employing pre-stress to generate finite cloaks for antiplane elastic waves
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.Comment: 4 pages, 2 figure
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