Misfit strain relaxation due to a viscous underlayer

The gradient of film force hfa x,t) along the length of the elastic film is balanced by the shear stress q x,t) acting on the interface between the film and the viscous layer, or 

For simple shear deformation in the viscous layer, the shear stress q(x,t) is proportional to the shearing rate in the layer, which is the speed of the top surface with respect to the bottom surface in a direction parallel to the interface, or 

This result makes clear the important influence of configuration size, as represented by a, on the relaxation process. For example, suppose that a = 1cm, Ei and hi = hy = 100 nm. The borosilicate glass at 800°C might have a viscosity as low as r]v = 10 N-s/m, in which case the characteristic time is roughly 10 s or about 10 days. A small metastable material structure held at elevated temperature for that length of time would lose its defining 

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