Geodesic
Numerical studies of the phase field model describing electric breakdown in a heterogeneous medium
Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 3, pp. 74-94 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper presents the results of numerical studies of the phase field model for the development of an electrical breakdown path. The model consists of Maxwell's equations in the quasi(electro)stationary approximation, the electric charge balance equation, and the Allen—Cahn equation describing the phase field evolution. Several problem settings concerning the development of a breakdown path in homogeneous as well as macro- and microheterogeneous media are considered.
Mots-clés : diffuse interface model
Keywords: phase field, order parameter, electric breakdown. 
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E. V. Zipunova; A. A. Kuleshov; E. B. Savenkov. Numerical studies of the phase field model describing electric breakdown in a heterogeneous medium. Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 3, pp. 74-94. http://geodesic.mathdoc.fr/item/SJIM_2024_27_3_a5/

[1] G. A. Vorob'ev, Yu. P. Pokholkov, Yu. D. Korolev, and V. I. Merkulov, Physics of Dielectrics (the Region of Strong Fields), Tomsk. Politekh. Univ., Tomsk, 2011 (in Russian)

[2] Pitike K. C., Hong W., “Phase-field model for dielectric breakdown in solids”, J. Appl. Phys., 115:4 (2014), 044101 | DOI

[3] Ambati M., Gerasimov T., De Lorenzis L., “A review on phase-field models of brittle fracture and a new fast hybrid formulation”, Comput. Mech., 55:2 (2015), 383–405 | DOI | MR | Zbl

[4] Zipunova E., Savenkov E., “Phase field model for electrically induced damage using microforce theory”, Math. Mech. Solids, 27:6 (2021) | DOI | MR

[5] Fried E., Gurtin M. E., “Continuum theory of thermally induced phase transitions based on an order parameter”, Physica, 68:3 (1993), 326–343 | DOI | MR | Zbl

[6] Gurtin M. E., “Generalized Ginzburg—Landau and Cahn—Hilliard equations based on a microforce balance”, Phisica D, 92:3 (1996), 178–192 | DOI | MR | Zbl

[7] Zipunova E., Savenkov E., “On the Diffuse Interface Models for High Codimension Dispersed Inclusions”, Mathematics, 9:18 (2021) | DOI

[8] Sargado J. M., Keilegavlen E., Berre I., Nordbotten J. M., “High-accuracy phase-field models for brittle fracture based on a new family of degradation functions”, J. Mech. Phys. Solids, 111 (2018), 458–489 | DOI | MR | Zbl