Numerical evaluation of the Eshelby tensor for a concave superspherical inclusion. (August 2015)

• Record Type: Journal Article
• Authors: Chen, Fengjuan; Giraud, Albert; Sevostianov, Igor; Grgic, Dragan
• Is Part Of: International journal of engineering science. Volume 93(2015:Aug.)
• Page Start: 51
• Page End: 58
• Publication Date: 2015-08
• Subjects: Eshelby tensor -- Supersphere -- Concave shape; Engineering -- Periodicals; Ingénierie -- Périodiques; Engineering; Periodicals; 620
• DOI: 10.1016/j.ijengsci.2015.04.007
• Languages: English
• ISSNs: 0020-7225

Abstract

Abstract: We calculate Eshelby tensor for inclusions of non-ellipsoidal shape. We focus on the superspherical shape described by equation x 2 p + y 2 p + z 2 p ⩽ 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 ).