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A general closed-form solution for elastic deformation of multilayers due to residual stresses and external bending is derived. Based on the general solution, simplified solutions for residual stress distributions in multiple layers of thin films on a thick substrate are obtained. These simplified solutions can be expressed as functions of either mismatch strains between film layers and substrate or the curvature of the system. The simplified solution for the special case of one film layer on a substrate is also presented, and its accuracy is discussed.
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Chun‐Hway Hsueh (2002) studied this question.
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