Eshelby tensors for an ellipsoidal inclusion in a micropolar material

Micropolar Eshelby tensors for an ellipsoidal inclusion are derived in an analytical form, which involves only one-dimensional integral. The numerical evaluation of the Eshelby tensors are also performed, it is found that the micropolar Eshelby tensors are not uniform in the ellipsoidal inclusion, however, their variations over the ellipsoidal domain are not significant. When size of inclusion is large compared to the characteristic length of the micropolar material, the micropolar Eshelby tensor is reduced to the classical one. It is also demonstrated that for a general ellipsoidal inclusion a uniform eigenstrain or eigentorsion produces on average only nonzero strain or torsion, and the average Eshelby relations are uncoupled.