Diffusion along a bi-material interface is complicated by the fact that different species are evolving under the influence of the same thermodynamic driving forces but at different rates. If the phases are assumed to be rigid this leads to the problem being over-determined. Relaxing this constraint so that the phases can deform elastically removes this problem. Diffusive creep deformation of a number of two-phase elastic systems with idealised geometries are analysed using differential and variational methods. If the connectivity of the phases is such that one phase cannot deform without the deformation of the other then the deformation rate is determined by the least mobile component. However, if this is not the case, such as for a distribution of precipitates within a polycrystalline matrix, it is principally the mobility of the matrix phase that determines the deformation rate
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