Effective Nonlinear AC Response To A Kind Of Graded Spherical Composites

Composites are doped by two or more materials that have different electrical conductivities, in which one or more types of inclusions are randomly embedded in the host in general, resulting in inhomogenetiy in the macroscopic scale. As a Composite, it can not only keeps the characteristics of each component material, but also generates new properties which individual component material do not have. As special composite materials, gradient composite materials have great potential in engineering application. Under an external electric field, the internal transport process of this material becomes extremely complex. Meanwhile, the application scope of gradient composite materials is greatly enlarged.In this paper, by using the perturbation method, the electric potential distribution, the effective nonlinear response of graded composites, in which a spherical particle is randomly embedded in a host, is studied under an external alternating-current (AC) electric field Eapp=E1sin ωt+E3sin3ωt with the constitutive relation of electric displacement and electric field Da=εαaE+χα|E|2E. The dielectric profile of the spherical inclusion is modeled by functionεi,(r)=ckrk(r≤α), where r is the radius of the spherical inclusion, and Ck, k, a are parameters. In the dilute limit, the electric potential distribution of graded composites is given in the inclusion region and host region, respectively. Meanwhile, the effective nonlinear response of graded composites and the general effective nonlinear response are also derived. Furthermore, comparison between effective nonlinear dielectric response and general effective nonlinear dielectric response is discussed. The main contents are as follows:1. A brief summary for the research significance, background and the present status of the graded composite and the research work of this thesis are given.2. Under an external AC electric field Eapp=E1sin ωt+E3sin3ωt, using the perturbation method, the electric potential distribution of the gradient composite is studied, in which a spherical particle is randomly embedded in a host, and its dielectric profile is modeled by function εi (r)=ckrk (r<α). The electric potential distribution of graded composites is given in the inclusion region and host region, respectively. 3. With the help of the Landau method, in the dilute limit, the effective dielectric response and the third-order nonlinear polarizability of the nonlinear gradient composite are studied. Moreover, the general effective nonlinear response are also derived and compared with the effective nonlinear response of graded composites.4. The research results of this thesis are summarized and discussed, and the outlook for further work is pointed out.