Related papers: Hyperelastic cloaking theory: Transformation elast…
The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…
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…
The nearly cloaking via transformation optics approach for the isotropic elastic wave fields is considered. This work extends the study of the nearly cloaking scheme to the elasticity system with residual stress in \mathbb{R}^{N} for N=2,3,…
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…
Transformation media theory, which steers waves in solids via an effective geometry induced by a refractive material (Fermat's principle of least action), provides a means of controlling vibrations and elastic waves beyond the traditional…
Elastic material with its elastic tensor losing minor symmetry is considered impossible without introducing artificially body torque. Here we demonstrate the feasibility of such material by introducing rotational resonance, the amplified…
An acoustic cloak envelopes an object so that sound incident from all directions passes through and around the cloak as though the object were not present. A theory of acoustic cloaking is developed using the transformation or…
The transformation method is a powerful tool for providing the constitutive parameters of the transformed material in the new coordinates. In transformation elasticity, a general curvilinear change of coordinates transforms conventional…
Cloaking elastic waves has, in contrast to the cloaking of electromagnetic waves, remained a fundamental challenge: the latter successfully uses the invariance of Maxwell's equations, from which the field of transformational optics has…
The invariance under co-ordinate transformations of a set of partial differential equations can lead to the possibility of invisibility cloaking, whereby an anomaly in the interior of a body is shielded from an external observer. The form…
The acoustic cloaking theory of Norris (2008) permits considerable freedom in choosing the transformation function f from physical to virtual space. The standard process for defining cloak materials is to first define f and then evaluate…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
A mathematical model for an elastoplastic continuum subject to large strains is presented. The inelastic response is modeled within the frame of rate-dependent gradient plasticity for nonsimple materials. Heat diffuses through the continuum…
Hyperelastic transformation method provides a promising approach to manipulate elastic waves by utilizing soft materials. However, no existing constitutive model can rigorously achieve the requirement of such method. In this Letter, a…
In this work, we develop a general mathematical framework on regularized approximate cloaking of elastic waves governed by the Lam\'e system via the approach of transformation elastodynamics. Our study is rather comprehensive. We first…
We study the approximate cloaking via transformation optics for electromagnetic waves in the time harmonic regime in which the cloaking device {\it only} consists of a layer constructed by the mapping technique. Due to the fact that…
It is known that design of elastic cloaks is much more challenging than the design idea for acoustic cloaks, cloaks of electromagnetic waves or scalar problems of anti-plane shear. In this paper, we address fully the fourth-order problem…
Randomly crosslinked macromolecules undergo a liquid-to-amorphous solid phase transition at a critical crosslink concentration. This transition has two main signatures: the random localization of a fraction of the monomers and the emergence…
An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically…
Metamaterials are constructed such that, for a narrow range of frequencies, the momentum density depends on the local displacement gradient, and the stress depends on the local velocity. In these models the momentum density generally…