A mixed electric boundary value problem for a two-dimensional piezoelectric crack |
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| Affiliation: | 1. Centre for Interdisciplinary Research in Basic Sciences, Jamia Millia Islamia, Jamia Nagar, New Delhi 110025, India;2. South African Medical Research Council Bioinformatics Unit, South African National Bioinformatics Institute, University of the Western Cape, Private Bag X17, Bellville, Cape Town 7535, South Africa;3. Laboratory of Computational Modeling of Drugs, South Ural State University, 76 Lenin prospekt, Chelyabinsk 454080, Russia |
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| Abstract: | In this paper, a mixed electric boundary value problem for a two-dimensional piezoelectric crack problem is presented, in the sense that the crack face is partly conducting and partly impermeable. By the analytical continuation method, the unknown electric charge distributions on the upper and lower conducting crack faces are reduced to two decoupled singular integral equations and then these two equations are converted into algebraic equations to find the full field solution. Though the results suggest that the stress intensity factors at the crack tip are identical to those of conventional piezoelectric materials, but the electric field and electric displacement are related to the electric boundary conditions on the crack faces. The electric field and electric displacement are singular not only at crack tips but also at the junctures between the impermeable part and conducting parts. Numerical results for the variations of the electric field, electric displacement field and J-integral with respect to the normalized impermeable crack length are shown. Some discussions for the energy release rate and the J-integral are made. |
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