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