We have begun to use numerical modeling to investigate how deformation patterns change as a rock melts. We do this by investigating in turn the different effects that we think melting a rock has on its rheology.
These models have been created in FLAC3D,
The mechanical materials are given an initial random distribution which reflects the probablity that each 'zone' within the model will melt and at what rate it will melt.

A: Our model is 10mm x 2mm, consisting of 100 x 40 zones. Each zone has a dimension of 0.1mm x 0.05mm . B: The velocity field, a general shear box in which x velocity is fixed along the top and bottom of the box, and the z velocity is fixed along the left and right edges.
Shear strain rate at the end of a model with a different initial random melting probablity distribution. Click on the figure to watch a movie of the development of partitioning of strain rate. Note that while the final distribution of strain is different from the above model, the amount of strain rate partitioning is similar.
Material strength is a linear function of the melt fraction and the grainsize squared. The grainsize is a function of strainrate