First-principles approach to conductivity of a nonlinear composite

Gu, Guoqing; Yu, Kin Wah; Hui, P. M.

doi:10.1103/physrevb.58.3057

Cited by 16 publications

(13 citation statements)

References 22 publications

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“…Thus, we have proposed a method for estimating the effective responses of random piezoelectric composites having the complex shapes of inclusions. Here, we should note that this method can be extended to study the piezoelectric composites having the nonlinear dielectric constituent, 20,21 and we believe that some interesting effective piezoelectric responses will be investigated, which is different from those of the linear piezoelectric composites. In the next work, we shall discuss effects of random piezoelectric composites containing inclusion shapes, inclusion arrangements, and anisotropic properties on the effective piezoelectric responses.…”

Section: Discussionmentioning

confidence: 99%

Effective properties of piezoelectric composites with periodic structure

et al. 2006

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The transformation field theory is developed to investigate the effective properties of piezoelectric composites consisting of anisotropic inclusions having arbitrary geometrical shapes in unit cell. The complicated boundary problem of arbitrary geometrical shapes of anisotropic inclusions is solved by introducing the transformation strain and electric fields. Motivated by theoretical investigation of the effective properties of piezoelectric composites, as an example, the effective dielectric, elastic, and piezoelectric constants of spherical periodic piezoelectric composites are discussed, and a good agreement is obtained by comparing the calculation results with the experimental data in the dilute limit.

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Section: Discussionmentioning

confidence: 99%

Effective properties of piezoelectric composites with periodic structure

et al. 2006

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“…(42) would be divergent if f A ≥ π/4 accounting for the overlapping inclusions. This formula has the same form as the one in linear electrical conduction which is not strange as they are both derived from periodic Laplace equations [250,251]. For electrical conduction with weak nonlinearity, the perturbation method and high-order Rayleigh identities can be developed to find the approximate analytical solution of temperature's high order small quantities [250].…”

Section: The Rayleigh Methodsmentioning

confidence: 99%

“…However, we have learned from periodic electromagnetic composites that the M&G and Bruggeman theories would give biased estimations in this situation due to the significant multipole interaction between the close inclusions [232]. The Rayleigh method was developed specifically to handle this dilemma, and has been used in photonic, phononic, and electric systems [232,[248][249][250]. If we consider two-dimensional infinite lattices in which circular inclusions (denoted as Material A again) are periodically arranged in the form of square lattices with a uniform thermal field (temperature gradient) applied along the x direction, then each unit cell containing one inclusion in the center could be treated equally under linear conduction as the temperature distribution in them should differ only by a constant.…”

Section: The Rayleigh Methodsmentioning

confidence: 99%

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Designing nonlinear thermal devices and metamaterials under the Fourier law: A route to nonlinear thermotics

Dai

2021

Front. Phys.

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Nonlinear heat transfer can be exploited to reveal novel transport phenomena and thus enhance people's ability to manipulate heat flux at will. However, there hasn't been a mature discipline called nonlinear thermotics like its counterpart in optics or acoustics to make a systematic summary of relevant researches. In the current review, we focus on recent progress in an important part of nonlinear heat transfer, i.e., tailoring nonlinear thermal devices and metamaterials under the Fourier's law, especially with temperature-dependent thermal conductivities. We will present the basic designing techniques including solving the equation directly and the transformation theory. Tuning nonlinearity coming from multi-physical effects, and how to calculate effective properties of nonlinear conductive composites using the effective medium theory are also included. Based on these theories, researchers have successfully designed various functional materials and devices such as the thermal diodes, thermal transistors, thermal memory elements, energy-free thermostats, and intelligent thermal materials, and some of them have also been realized in experiments. Further, these phenomenological works can provide a feasible route for the development of nonlinear thermotics.

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“…It is also possible to develop a method for studying the effective nonlinear dielectric response of graded piezoelectric composites by further development on some existing methods for solving nonlinear composites problems. [29][30][31][32] …”

Section: Discussionmentioning

confidence: 99%

Dielectric response of spherically anisotropic graded piezoelectric composites

Wei

Poon

et al. 2007

Journal of Applied Physics

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A graded piezoelectric composite consisting of a spherically anisotropic graded piezoelectric inclusion imbedded in an infinite nonpiezoelectric matrix, with the physical properties of the graded spherical inclusion having a power-law profile with respect to the radial variable r, is studied theoretically. Under an external uniform electric field, the electric displacement field and the elastic stress tensor field of this spherically anisotropic graded piezoelectric composite are derived exactly by means of displacement separation technique, based on the governing equations in the dilute limit. A piezoelectric response mechanism, in which the effective piezoelectric response vanishes along the z direction ͑or x,y directions͒, is revealed in this kind of graded piezoelectric composites. Furthermore, it is found that the effective dielectric constant decreases ͑or increases͒ with the volume fraction p of the inclusions if the exponent parameter k of the grading profile is larger ͑or smaller͒ than a critical value.

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First-principles approach to conductivity of a nonlinear composite

Cited by 16 publications

References 22 publications

Effective properties of piezoelectric composites with periodic structure

Effective properties of piezoelectric composites with periodic structure

Designing nonlinear thermal devices and metamaterials under the Fourier law: A route to nonlinear thermotics

Dielectric response of spherically anisotropic graded piezoelectric composites

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