Abstract
The three-dimensional problem of an elliptic crack located at the interface between two bonded dissimilar elastic half-spaces and crack faces subjected to normal pressure equal in magnitude and opposite in direction is considered here. Considering a Cartesian coordinate system with the xOy-plane coinciding with the crack plane and origin O coinciding with the crack centre, the mixed boundary conditions on the \(z=0\) plane give rise to three pairs of dual integral equations. This typical mixed boundary value problem is solved here analytically for the first time for normal pressure prescribed on the crack faces. With uniform normal pressure, the three pairs of dual integral equations are reduced to two sets of dual integral equations, which further reduce to a Cauchy singular integral equation that is solved using Plemelj formula. The present work opens up the possibility of further research work in the field of interface elliptic crack located at the interface of bonded elastic or piezoelectric solids.
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Acknowledgments
The first author (T.K. Saha) acknowledges the University Grants Commission of India for awarding a Minor Research Project (PSW-149/11-12 (ERO)). The authors also gratefully acknowledge the reviewer for the constructive comments.
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Saha, T.K., Roy, A. (2015). On an Interface Elliptic Crack. In: Sarkar, S., Basu, U., De, S. (eds) Applied Mathematics. Springer Proceedings in Mathematics & Statistics, vol 146. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2547-8_28
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DOI: https://doi.org/10.1007/978-81-322-2547-8_28
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