Constant gradient in mismatch strain

the case of a film with a constant gradient in mismatch strain is considered, that is, the case of a film for which 

For the present example, it will be assumed that Mf z) = M, a constant, throughout the film. In this case, / = etopMf/if. 

If the curvature given by (2.51) is evaluated for the linearly varying mismatch strain (2.59) and constant film stiffness Mf, then 

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