The estimate of permittivity of anisotropic composites with lamellar inclusions by the self-assessment method
<p>Composites are widely used as structural or thermal protection materials; they are used as well as functional materials in a large number of different electrical devices and as dielectrics. This composite has one of the most important characteristics the relative permittivity. It depends pr...
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| Format: | Article |
| Language: | Russian |
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MGTU im. N.È. Baumana
2015-01-01
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| Series: | Matematika i Matematičeskoe Modelirovanie |
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| Online Access: | http://mathm.elpub.ru/jour/article/view/12 |
| _version_ | 1818929773606338560 |
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| author | V. S. Zarubin G. N. Kuvyrkin O. V. Pugachev |
| author_facet | V. S. Zarubin G. N. Kuvyrkin O. V. Pugachev |
| author_sort | V. S. Zarubin |
| collection | DOAJ |
| description | <p>Composites are widely used as structural or thermal protection materials; they are used as well as functional materials in a large number of different electrical devices and as dielectrics. This composite has one of the most important characteristics the relative permittivity. It depends primarily on the dielectric properties of the inclusions and the matrix as well as the shape and volume content of the inclusions.<br />In this paper, a mathematical model of the interaction of the electrostatic fields in an isotropic plate and in the surrounding homogeneous anisotropic medium is constructed. This model describes the dielectric properties of the composite with such inclusions. A variant of the same orientation of lamellar inclusions is considered, which leads to the special case of anisotropy of the dielectric properties of the composite that has transverse isotropy towards the direction perpendicular to the inclusions. The shape of inclusions is represented as an oblate ellipsoid of revolution (spheroid). Transformation of the differential equation describing the distribution of the electric potential transversely to isotropic medium surrounding the spheroidal inclusion, to the Laplace equation with the subsequent transition from the initial spheroid to the given ellipsoid of rotation allows us to apply the self-assessment method for the determination of the dielectric properties of the composite. This method equates the result of averaging the perturbation of the electrostatic field in the inclusions and the matrix particles towards the unperturbed fields in the environment to zero.<br />The constructed mathematical model allows us to determine the electrostatic field disturbance in the inclusions and the matrix particles towards the unperturbed field given in the environment at a distance from the inclusions and the matrix particles, much larger than their characteristic dimensions. By averaging the perturbation of the electrostatic field in all the elements of the composite structure, a system of two quadratic equations for the desired principal values of the permittivity tensor of the composite is obtained. Results of this quantitative analysis are shown in graphs and can be used to predict the dielectric characteristics of composites with identically oriented lamellar inclusions (including in the form of nanostructured elements).</p> |
| first_indexed | 2024-12-20T03:50:08Z |
| format | Article |
| id | doaj.art-3e71ce8f75f14465b86923e8a3dad2de |
| institution | Directory Open Access Journal |
| issn | 2412-5911 |
| language | Russian |
| last_indexed | 2024-12-20T03:50:08Z |
| publishDate | 2015-01-01 |
| publisher | MGTU im. N.È. Baumana |
| record_format | Article |
| series | Matematika i Matematičeskoe Modelirovanie |
| spelling | doaj.art-3e71ce8f75f14465b86923e8a3dad2de2022-12-21T19:54:29ZrusMGTU im. N.È. BaumanaMatematika i Matematičeskoe Modelirovanie2412-59112015-01-0101364811The estimate of permittivity of anisotropic composites with lamellar inclusions by the self-assessment methodV. S. Zarubin0G. N. Kuvyrkin1O. V. Pugachev2Bauman Moscow State Technical University, RussiaBauman Moscow State Technical University, RussiaBauman Moscow State Technical University, Russia<p>Composites are widely used as structural or thermal protection materials; they are used as well as functional materials in a large number of different electrical devices and as dielectrics. This composite has one of the most important characteristics the relative permittivity. It depends primarily on the dielectric properties of the inclusions and the matrix as well as the shape and volume content of the inclusions.<br />In this paper, a mathematical model of the interaction of the electrostatic fields in an isotropic plate and in the surrounding homogeneous anisotropic medium is constructed. This model describes the dielectric properties of the composite with such inclusions. A variant of the same orientation of lamellar inclusions is considered, which leads to the special case of anisotropy of the dielectric properties of the composite that has transverse isotropy towards the direction perpendicular to the inclusions. The shape of inclusions is represented as an oblate ellipsoid of revolution (spheroid). Transformation of the differential equation describing the distribution of the electric potential transversely to isotropic medium surrounding the spheroidal inclusion, to the Laplace equation with the subsequent transition from the initial spheroid to the given ellipsoid of rotation allows us to apply the self-assessment method for the determination of the dielectric properties of the composite. This method equates the result of averaging the perturbation of the electrostatic field in the inclusions and the matrix particles towards the unperturbed fields in the environment to zero.<br />The constructed mathematical model allows us to determine the electrostatic field disturbance in the inclusions and the matrix particles towards the unperturbed field given in the environment at a distance from the inclusions and the matrix particles, much larger than their characteristic dimensions. By averaging the perturbation of the electrostatic field in all the elements of the composite structure, a system of two quadratic equations for the desired principal values of the permittivity tensor of the composite is obtained. Results of this quantitative analysis are shown in graphs and can be used to predict the dielectric characteristics of composites with identically oriented lamellar inclusions (including in the form of nanostructured elements).</p>http://mathm.elpub.ru/jour/article/view/12compositepermittivitylamellar inclusions |
| spellingShingle | V. S. Zarubin G. N. Kuvyrkin O. V. Pugachev The estimate of permittivity of anisotropic composites with lamellar inclusions by the self-assessment method Matematika i Matematičeskoe Modelirovanie composite permittivity lamellar inclusions |
| title | The estimate of permittivity of anisotropic composites with lamellar inclusions by the self-assessment method |
| title_full | The estimate of permittivity of anisotropic composites with lamellar inclusions by the self-assessment method |
| title_fullStr | The estimate of permittivity of anisotropic composites with lamellar inclusions by the self-assessment method |
| title_full_unstemmed | The estimate of permittivity of anisotropic composites with lamellar inclusions by the self-assessment method |
| title_short | The estimate of permittivity of anisotropic composites with lamellar inclusions by the self-assessment method |
| title_sort | estimate of permittivity of anisotropic composites with lamellar inclusions by the self assessment method |
| topic | composite permittivity lamellar inclusions |
| url | http://mathm.elpub.ru/jour/article/view/12 |
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