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Numerical solution for a crack embedded in multiple elliptic layers with different elastic properties

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Abstract

The medium is composed of an elliptic inclusion and many confocal elliptic layers. The crack is embedded in the elliptic inclusion. The remote loading is applied at the remote place of the matrix. Complex variable method and conformal mapping are used to study the mentioned problem. This paper provides a numerical solution for the mentioned crack problem. The continuity condition for the traction and displacement along the interface is reduced to a relation of two sets of Laurent series coefficients for the complex potentials defined in the interior or exterior to the interface. This formulation is called the matrix transfer method in this paper. From the following three conditions, the traction-free condition along creak face, the continuity condition for the traction and displacement along the interfaces and the remote loading condition, the problem is finally solved. Servable numerical examples are provided. For the exterior finite matrix case, the relevant solution is also provided.

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Authors and Affiliations

  1. Division of Engineering Mechanics, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Y. Z. Chen

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  1. Y. Z. Chen
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Correspondence to Y. Z. Chen.

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Chen, Y.Z. Numerical solution for a crack embedded in multiple elliptic layers with different elastic properties. Acta Mech 226, 2807–2829 (2015). https://doi.org/10.1007/s00707-015-1351-1

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  • DOI: https://doi.org/10.1007/s00707-015-1351-1

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