Numerical evaluation of the Eshelby tensor for a concave superspherical inclusion

We calculate Eshelby tensor for inclusions of non-ellipsoidal shape. We focus on the superspherical shape described by equation x2p+y2p+z2p⩽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).