Multi-Scale Methods in Simulation—A Path to a Better Understanding of the Behaviour of Structures

  • Michael HackEmail author
Part of the Mathematical Engineering book series (MATHENGIN)


Efficient and accurate simulation methods are key for all development processes in all industries. Without simulation all influences of design changes, material choices, load situations, etc., on the performances of parts, sub-systems and systems, need to be confirmed by time consuming and expensive test procedures. On the other hand, including these influences into the design process by simulation together with efficient optimisation strategies allows to balance different performances, while allowing cost-efficient and ecological manufacturing as well as keeping a low weight of the complete system at the same time. To gain accurate results in a simulation, it is not sufficient to just model the geometry correctly; a main challenge is to model the material behaviour correctly. State of the art for metal based structures is to use material data that have been gained in experiments. Especially for fatigue performances, the expected lifetime fatigue material data is derived from databases or so called material laws. This approach does not take into account any manufacturing influences, even though these can locally lead to much improved behaviour. Therefore these parts are often still over-designed with respect to fatigue. For composite materials this approach is not even valid anymore as the behaviour strongly depends on the manufacturing process. Those influences can be analysed if one looks closer, i.e. at a different scale. The behaviour at the smaller scale then defines the material behaviour at the global scale. This process may even be recursive: even smaller scales are needed for the behaviour of intermediate scales—even down to atomistic levels. It is clear that such approaches can lead to tremendous computational cost. Therefore it is a key need to keep the process efficient, on one hand by analysing the methodologies on each scale, on the other hand by intelligent choice of the best method at each location.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Siemens PLM SoftwareKaiserslauternGermany

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