An alternative model for elastic bending deformation of multilayered beams

Abstract

An exact closed-form solution for elastic deformation of multilayered beams due to residual stresses and external bending is derived in terms of the normal strain at the centroidal principal axis and the curvature radius of the neutral axis for zero normal strain. Two approximate models for the case of multilayered films on a thick substrate are obtained. For a bilayered beam, the exact solution can be expressed in terms of the mismatch stress between the film and the substrate, the thickness ratio, and the modulus ratio. The reduction error analysis for the two approximations is applied.