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When exposed to an external solvent, a dry polymeric network imbibes the solvent and undergoes large deformation. The resulting aggregate is known as a hydrogel. This swelling process is diffusion driven and thus results in differential swelling during transient swelling. When subjected to external geometrical constraints, such as being rigidly fixed or attachment to a compliant substrate, wrinkles have been shown to appear due to mechanical instabilities. In the case of free swelling, there are no external constraints to induce the instabilities accounting for wrinkling patterns. However, during the transient swelling process, the swelling differential between the gel on the exterior and the interior causes compressive stresses and gives rise to mechanical instabilities. It is also observed that the time dependence of the swelling profile causes the wrinkles to evolve with time. In this work, we investigate this interesting phenomenon of transient wrinkle mode evolution using the finite element and state-space methods. From our simulations and prediction, we find that there is an inverse relation between critical wave number and time, which has earlier been observed in experiments.

In conventional analyses of composite laminates, the assumption of perfect bonding of adjoining layers is well accepted, although this is an oversimplification of the reality. It is possible that the bond strength may be less than that of the laminae. Thus, the study of weak bonding is an interesting focus area. In this study, an elastic bonding model based on three-dimensional theory of elasticity in a layerwise framework is used to study composite laminates. The differential quadrature (DQ) discretization is used to analyze the layerwise model. The present model enables the simulation of actual bonding stress states in laminated structures. The interfacial characteristics of transverse stress continuity as well as the kinematic continuity conditions are satisfied through the inclusion of the elastic bonding layer. The present model is employed to investigate the free vibration of thick rectangular cross-ply laminates of different boundary conditions and lamination schemes.