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numerical methods for multiscale problems

 

     
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  Marcel Arndt, Michael Griebel : Multiscale atomistic-continuum simulation of shape memory alloys

Materials often show complex behaviour which needs to be resolved on different length scales. For example, certain microscopic effects can be described on an atomistic level using molecular dynamics, whereas macroscopic effects can be modelled on the continuum mechanical level. However, a direct numerical treatment of the coarser scale is usually not possible due to computational limits. To this end, advanced analytical and numerical techniques are needed to bridge the gap between the different scales. Here, we discuss the transition from the atomistic to the continuum mechanical level using techniques from statistical mechanics and multiscale analysis, where both scales are combined into one model simultaneously. We consider the example of crystalline microstructure in shape memory alloys to demonstrate our approach and show the results of various numerical experiments.
Impressum
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