Numerical calculations of an effective elasticity tensor and extremal stresses for arbitrary magnet composites

For the calculation of mechanical properties of large magnet systems in 3-dimensional space, a very fine subdivision of the magnetstructure is necessary. In the finite element programms, this will lead to unacceptably long computing times and to the limits of computer-storage capacity. This limitation requires a simplification of the structure model. The objective of this work is to find such simplifications that yield still reliable results by the stress-strain analysis. This problem can be solved by the numerical method, called 'numerical simulation', by which an effective elasticity tensor will be obtained for a composite material. The structure can be arbitrarily complicated and may contain voids, e.g. cooling channels, which are weak elements for the structural analysis. The structure has to perform only a homogeneity-condition, i.e. it must be possible to define a 'representative volume element' (RVE). With the effective elasticity tensor, which can be found for such RVE, it is possible to calculate the average stress and with the surface displacement method also the extremal stresses in each point of the structure. It is found a good agreement between experimental and theoretical moduli of elasticity. (orig.)