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A cross-scale homogenization approach for multi-phase materials is to calculate an effective material stiffness in the smaller scale for the multiple states. These detailed results are used to identify a calculation rule for the effective material stiffness in the larger scale. The calculation of the stiffness matrix using ABAQUS for 3D finite elements was already described by [1]. This can be transferred to the calculation of the 2D stiffness matrix in R 3×3 without much effort. However, some 2D elements in ABAQUS require the specification of a matrix in R 4×4. In this article, the methods for calculating this type of stiffness matrix in 2D are presented.