Numerical evaluation of the Eshelby tensor for a concave superspherical inclusion

Abstract : We calculate Eshelby tensor for inclusions of non-ellipsoidal shape. We focus on the superspherical shape described by equation X-2P + y(2p) + Z(2p) <= 1. It is convex when p > 0.5 and concave when p < 0.5. We propose a numerical approach to perform: integration on the surface of the superspherical inclusion necessary to compute the average Eshelby tensor. Validation of the method is done by comparison of the results with analytical solutions for a spherical inclusion (p = 1) and with numerical results of Onaka (2001) (p > 1).
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https://hal.univ-lorraine.fr/hal-01276856
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Submitted on : Saturday, February 20, 2016 - 5:44:09 PM
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Fengjuan Chen, Albert Giraud, Igor Sevostianov, Dragan Grgic. Numerical evaluation of the Eshelby tensor for a concave superspherical inclusion. International Journal of Engineering Science, Elsevier, 2015, 93, pp.51-58. ⟨10.1016/j.ijengsci.2015.04.007⟩. ⟨hal-01276856⟩

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