Stress Relaxation Analysis in Viscoelastic Adhesive Layers of the Five-Layer Sandwich Plate with Functionally Graded Face Sheets

In this study, the layerwise theory, along with the first-order shear deformation theory, was employed to investigate the relaxation of stresses in the adhesive layers of a symmetric five-layer square sandwich plate subjected to a uniformly distributed load. The functionally graded face sheets were bonded to the homogeneous core using two thin layers of viscoelastic adhesive. Using the principle of virtual work, the governing equations were derived and transformed into the Laplace domain. The displacement fields were then obtained by applying the Navier solution and converted back to the time domain using the numerical inverse Laplace transform. The results were verified through finite element analysis, showing good agreement between the two approaches. Both methods revealed that the in-plane and out-of-plane stress components remain almost constant across the adhesive thickness but have considerable magnitudes. Additionally, the maximum adhesive planar stresses σ and τ are highly dependent on the magnitude of the adhesive elastic modulus, power index, and viscoelastic properties of the adhesive layer. Therefore, it was concluded that for a safe design in thin sandwich plates, the presence of viscoelastic adhesive layers must be considered in the formulation and their effect should not be ignored.