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The purpose of this paper is to present new expressions in Cartesian coordinates for the potential and magnetic field of prolate and oblate spheroids with arbitrary direction of the symmetry axis in a homogeneous field.

The potentials found in prolate or oblate spheroidal coordinates are transformed to Cartesian coordinates. These results are represented in such a form that they depend only on expressions, which are invariant under rotations around the symmetry axis. Thus, it is easy to change to arbitrary directions of both the symmetry axis and of that of the primary field. The gradients of the potentials are calculated and transformed exactly to the simplest form possible.

The paper presents simple expressions for the magnetic perturbations due to homogeneous prolate or oblate spheroids in a homogeneous magnetic field.

Results are exact for single non‐ferromagnetic spheroids in a homogeneous field.

Superposition of these perturbations presupposes small values of the magnetic susceptibilities of both the spheroids and their environment as in biological tissues.

The paper presents novel formulas for fields of homogeneous spheroids in a homogeneous magnetic field which are very useful for modelling biological tissues in studies of magnetic resonance imaging and magnetic resonance spectroscopy.

The purpose of this study is to quantify the impact of the variation of microstructural features on macroscopic and microscopic fields. The application of multi-scale methods in the context of constitutive modeling of microheterogeneous materials requires the choice of a representative volume element (RVE) of the considered microstructure, which may be based on some idealized assumptions and/or on experimental observations. In any case, a realistic microstructure within the RVE is either computationally too expensive or not fully accessible by experimental measurement techniques, which introduces some uncertainty regarding the microstructural features.

In this paper, a systematical variation of microstructural parameters controlling the morphology of an RVE with an idealized microstructure is conducted and the impact on macroscopic quantities of interest as well as microstructural fields and their statistics is investigated. The study is carried out under macroscopically homogeneous deformation states using the direct micro-macro scale transition approach.

The variation of microstructural parameters, such as inclusion volume fraction, aspect ratio and orientation of the inclusion with respect to the overall loading, influences the macroscopic behavior, especially the micromechanical fields significantly.

The systematic assessment of the impact of microstructural parameters on both macroscopic quantities and statistics of the micromechanical fields allows for a quantitative comparison of different microstructure morphologies and a reliable identification of microstructural parameters that promote failure initialization in microheterogeneous materials.