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Linear Inclusion and Related Problems

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Theory of Electroelasticity

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Abstract

In this chapter, the linear cracks and inclusions are discussed. These problems are mainly reduced to vector Riemann-Hilbert boundary problem with many variables at first, and then the standard method to solve the Riemann-Hilbert boundary problem is used. In general case, the numerical computation is used to get the final results due to its complexity, but for some simpler problems, the analytical solutions can also be obtained. The interface cracks, rigid inclusion, and electrodes in piezoelectric bimaterials are discussed in detail. Some special problems, such as partly insulated and partly conducting crack, the nonideal crack and some other models in a homogeneous piezoelectric material, and contact zone model for interface cracks in a piezoelectric bimaterial, are also discussed shortly. Some interesting problems in engineering, such as interaction of collinear inclusions with singularity loading, interaction of an elliptic hole and a vice-crack, strip electric saturation model of an impermeable crack in a homogeneous material and a strip electric saturation model for mode-III interface crack in a bimaterial, and mode-III problem for a circular inclusion with interface cracks, are also discussed.

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Authors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China, People’s Republic

    Zhen-Bang Kuang

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  1. Zhen-Bang Kuang
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© 2014 Shanghai Jiao Tong University Press, Shanghai and Springer-Verlag Berlin Heidelberg

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Kuang, ZB. (2014). Linear Inclusion and Related Problems. In: Theory of Electroelasticity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36291-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-36291-0_4

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  • Print ISBN: 978-3-642-36290-3

  • Online ISBN: 978-3-642-36291-0

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