Plane-strain deformation of multilayer structures under normal surface loading

The deformation of multilayer structures under external loadings provides both opportunities and challenges for modern manufacture. The stress and displacement fields are influenced by the structure’s geometrical configuration, material properties, and bonding conditions at the interfaces between adjoining layers. In this study, we investigate the mechanical response of a perfectly-bonded multilayer structure under normal loading using the Fourier transform. The normal loading is decomposed into symmetric and antisymmetric cases based on the linear superposition principle. Closed-form solutions are obtained in the formation of Fourier integrals with the associated coefficients being determined by the boundary conditions. The effects of Poisson’s ratio, shear modulus, and thickness on the stress distribution and maximum displacement are studied. For a two-layer structure, plastic deformation is most likely to initiate in the soft layer near the interface in the presence of a large shear moduli ratio between the two layers. Although the average normal displacement increases as the soft layer thickens, regardless of the shear modulus ratio, it may not increase monotonically with the total thickness, particularly when the shear modulus ratio is small. Under the thin film approximation, the response with uniform normal loading can be used to estimate the response of the indentation problem. The numerical model presented in this work provides a tool to analyze the deformation of multilayer structures under surface loadings.