On computation of the compliance and stiffness contribution tensors of non ellipsoidal inhomogeneities

We discuss computation of compliance/stiffness contribution tensors of an inhomogeneity of non-ellipsoidal shape and the difficulties that may be encountered in this context. These issues are illustrated on the example of one specific shape factor: concavity–convexity of the inhomogeneity shape. It is found, in particular, that the effect of the concavity factor depends on the specific constraint imposed. If the inhomogeneity volume is kept constant, then its compliance contribution rapidly increases with increasing concavity; on the computational side it leads to difficulties related to unusually high requirements to the accuracy of the computed volume averages quantities. If, on the other hand, the characteristic dimensions (for example, the distance between the farthest points) are kept constant, then the dependence of the compliance contribution on the concavity factor is almost linear.