Thermoelastic cloaking and the breaking of invisibility

Abstract

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 invariance of the equations of thermoelasticity under a class of transformations between reference configurations is demonstrated, with implications for thermal and thermoelastic invisibility cloaking discussed. Specifically, the theory of thermoelasticity is found to not allow for invisibility cloaking, similarly to elastodynamics. Thermal invisibility cloaking is therefore broken by coupling to mechanics. In the case of weakly coupled linear thermoelasticity, measurements of temperature by external observers are shown to be perturbed by the weak thermomechanical coupling, but only to second order in the degree of coupling. This implies the phenomenon of approximate invisibility, meaning that a thermal cloaking device with weak coupling to mechanics could maintain near-perfect cloaking.

Dual-function thermoelastic cloak based on coordinate transformation theory

“…( 68) and (69) given in Ref. [ 36 ]. This does not imply the commonality of coordinate transformation theory and incremental theory, however, as both theories have obvious different physical meanings.…”

“…In the field of high-speed PCBs 30 or chips 31 , heat concentration 32,33 and the excitation of elastic waves 34,35 have attracted much attention. Syvret et al 36 analyzed the possible breaking of thermal invisibility caused by coupling effect, illustrating the shortcomings of existing single function cloaks in a coupled field. Li et al 37 provided a design for a dual-function transformation cloak with simultaneous heat flow and electric field regulation.…”

Transformation Cloaking in Elastic Plates

“…The idea of cloaking has been thoroughly studied and is well understood in the context of conductivity [Greenleaf et al, 2003a,b], electrical impedance tomography and electromagnetism [Bryan and Leise, 2010, Greenleaf et al, 2007. The possibility of cloaking has been examined in many other fields of science and engineering, e.g., acoustics [Chen and Chan, 2007, Farhat et al, 2008,b, Norris, 2008, Cummer et al, 2008a,b, Zhou et al, 2008, optics [Leonhardt and Philbin, 2012], thermodynamics (i.e., design of thermal cloaks) [Guenneau et al, 2012, Han et al, 2014, diffusion [Guenneau and Puvirajesinghe, 2013], quantum mechanics [Zhang et al, 2008], thermoelasticity [Syvret andAl-Attar, 2019, Hostos et al, 2019], seismology Crawford, 2016, Sklan et al, 2018], and elastodynamics [Milton et al, 2006, Parnell, 2012 (see the recent reviews [Kadic et al, 2013, Koschny et al, 2017 for a discussion of these applications in some detail). Recently, we formulated both the nonlinear and linearized elastodynamic transformation cloaking problems (in 3D) in a mathematically precise form [Yavari and Golgoon, 2019].…”