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Electrically and magnetically induced Maxwell stresses in a magneto-electro-elastic medium with periodic limited permeable cracks

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Abstract

In this work, the Maxwell stresses arising due to an electric and a magnetic field both at the crack faces and infinity are taken into account to determine and analyse some main fracture parameters for a periodic system of cracks in a magneto-electro-elastic material. A plane strain problem is formulated and analysed. At the crack faces, the limited permeable electromagnetic boundary conditions are assumed. The material is subjected to a relatively weak mechanical and a strong electric and magnetic loading applied at infinity. The solution of the problem is obtained in a closed form using a complex function theory. Formulas for stresses, magnetic induction and electric displacement vector, elastic displacements, magnetic and electric potential jumps at the interface as well as the intensity factors at the crack tips are presented as relatively simple analytical expressions. The system of two cubic equations is obtained for the electric displacement and magnetic induction in the crack regions. A case of a single limited permeable crack in a magneto-electro-elastic medium is studied as well, and the results related to this case and to the periodic crack set are compared.

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Acknowledgments

This work has been partially carried out within the framework of the Transversal Program of the Pascal Institute, Division “Materials and Multiscale Modeling” and of the Excellence Laboratory LabEx IMobS3 (ANR-10-LABX-16-01) (supported by the French program investissement d’avenir and managed by the National Research Agency (ANR), the European Commission (Auvergne FEDER funds) and the Region Auvergne), which is gratefully acknowledged.

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Authors and Affiliations

  1. Institut Pascal/UBP/IFMA/CNRS/Clermont Université, BP 20265, 63175, Aubière Cedex, France

    O. Viun

  2. Department of Theoretical and Applied Mechanics, Dnipropetrovsk National University, Dnipropetrovsk, Ukraine

    V. Loboda

  3. French Institute of Advanced Mechanics, Institut Pascal/UBP/IFMA/CNRS/Clermont Université, BP 265, 63175, Aubière Cedex, France

    Y. Lapusta

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  1. O. Viun
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  2. V. Loboda
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  3. Y. Lapusta
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Correspondence to O. Viun.

Appendix

Appendix

Table 2 Effective properties of \(\hbox {BaTiO}_{3}\) – \(\hbox {CoFe}_{2}\hbox {O}_{4}\) material for different \(V_\mathrm{f}\) (Sih and Song [22])
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Viun, O., Loboda, V. & Lapusta, Y. Electrically and magnetically induced Maxwell stresses in a magneto-electro-elastic medium with periodic limited permeable cracks. Arch Appl Mech 86, 2009–2020 (2016). https://doi.org/10.1007/s00419-016-1166-0

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