This doctoral thesis focuses on the investigation of the evolution of quasi-periodic deformation patterns (wrinkles) in multi-layered viscoelastic structures with thin layers subjected to compressive loads. Despite the significance of these structures in technology and medicine, their behaviour has been poorly studied so far due to the challenges in analyzing the interactions between viscoelastic and nonlinear effects during the development of deformations. In this research, we developed a theory of visco-hyperelasticity, an intrinsic theory of beams on elastic foundations, and a new reduced theory of shells. Additionally, a novel spherical spectral method was developed for solving the shell equations.
Alongside the theoretical work, we also developed new experimental approaches. These include a method for analyzing the wrinkling of a simple compressively loaded film on a flat substrate, which softens under deformation, and a method for analyzing the evolution of deformation in a compressively loaded spherical elastic film on a viscoelastic substrate. Using the developed methods, we demonstrated that the loading rate has a significant impact on the final deformation state, as structures can become trapped in metastable so-called ``frozen'' states. Furthermore, we showed that due to the interaction between nonlinear and viscoelastic effects, only quasi-periodic deformation patterns emerge in the studied structures, which are not attainable in purely elastic structures.
Using analytic, numeric and experimental techniques the findings were validated on both complex and simpler structures, where the mentioned phenomena are less pronounced but still present.
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