![]() ![]() This coupling between the scales corresponds to a serial, hand-shake type exchange of data (e.g. The corresponding technique is known as the localization method. Alternatively, in process modeling it is important to be able to step down to the scale of the real, heterogeneous material microstructure. In the case of multi-scale material modeling and in homogenization in general, one proceeds from the detailed description of all material heterogeneities at the lower scale upward in order to obtain effective material properties accurately. Bridging the scales is an essential feature of the multi-scale analysis of components with locally different material properties 1. Each of them allows the tailoring of the microstructure in order to achieve the desired functionality. For many industrial applications the final material properties result from a number of process steps. Material properties characterize the functionality of almost any product. \renewcommand Introduction ¶ Multi-scale analysis of components with a heterogeneous microstructure ¶
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