A new front-tracking method to model anisotropic grain and phase boundary motion in rocks

Microstructures of rocks play an important role in determining rheological properties and help to reveal the processes that lead to their formation. Some of these processes change the microstructure significantly and may thus have the opposite effect in obliterating any fabrics indicative of the previous history of the rocks. One of these processes is grain boundary migration (GBM). During static recrystallisation, GBM may produce a foam texture that completely overprints a pre-existing grain boundary network and GBM actively influences the rheology of a rock, via its influence on grain size and lattice defect concentration.In this paper we present a new front-tracking method to simulate GBM. Generally, any movement of boundaries is driven by the minimisation of the internal free energy of a system. The new method moves boundaries along the energy gradient towards a lower total energy state of the system. The calculation of the energy gradient is not necessarily limited to (an)isotropic boundary energies but may also include metamorphism, melting, reaction energies, surface energies and elastic stresses, etc. Two examples are included in this paper where we simulate grain growth with isotropic boundary energy functions and grain growth with isotropic and anisotropic boundary energy functions in a system with a melt present.