Transient response of bilayered elastic strips with interfacial diffusion and sliding in cylindrical bending

Abstract

Time-dependent deformations of bilayered elastic strips with interfacial diffusion and sliding in cylindrical bending are studied. A film–substrate system is also addressed by letting the thickness of one layer approach infinity. Our solution clearly indicates that the stresses and displacements in the strip evolve with two relaxation times when its upper surface is subjected to a sinusoidal pressure. Explicit and elementary expressions of the relaxation times are derived. The steady-state displacement jumps across the interface are found independent of the elastic property and thickness of the lower layer free of external loading. When the film is extremely thin, the relaxation times are independent of the elastic property of the substrate; when the film is extremely thick, the relaxation times are found independent of the film thickness. Detailed numerical results are presented to show the influence of the material, geometric and interface parameters on the relaxation times and on the evolving displacements and stresses in the strip or in the film–substrate system. Finally, the state-space method is proposed to determine the transient elastic field in simply supported multilayered elastic strips with interfacial diffusion and sliding under thermomechanical loads.

Transient responses of laminated anisotropic piezothermoelastic plates and cylindrical shells with interfacial diffusion and sliding in cylindrical bending

“…The state equation of the relative sliding displacements with respect to the time variable was derived by Yan et al [7] to investigate the time-dependent behavior of a simply supported, angle-ply piezoelectric laminate with viscoelastic interfaces. Wang and Wang [8] derived an exact solution for a multilayered isotropic elastic strip with simultaneous interfacial diffusion and sliding under thermomechanical loading. By using the transfer matrix and state-space methods, Wang and Schiavone [9] derived an exact solution for the time-dependent deformations of a multilayered orthotropic elastic strip with interfacial diffusion and sliding under mechanical loading.…”