Bifurcation phenomenon in bi-layered system with thin films and its application in the development of stretchable bendable devices

"Bifurcation of equilibrium" is a term that is used to describe the condition in which a system admits multiple solutions to the equilibrium problem, in other words has multiple possible deformed configurations that can be considered equilibrated under the same load, usually referred to as the critical load. The loss of uniqueness of the equilibrium problem, also results in a loss of stability of the system, which is because the equilibrated configuration that is unstable becomes energetically more favorable over the stable one. An unstable equilibrated configuration can be described as a configuration in which a small change in parameter values, for example a small perturbation in the load or a small defect in the geometry of the system, will lead to a large change in the behavior of the system that can often be catastrophic for the system itself, one example of this is the buckling of a beam. Conventionally due its disruptive nature, instability is considered undesirable. For this reason, in the past few decades a lot of studies have focused on modeling and predicting the onset of instability in many systems and under many loading conditions. Since bifurcation events are specific for each system, namely are unique after the system is defined, some studies have had the intention to employ this information to learn more about specific systems. For example, several studies have focused on understanding how changing the material properties of a system can affect the onset of instability. The knowledge gained from that can also be employed to solve the inverse problem - in other words, if we identify the instability onset, we can use this information as a means to evaluate the mechanical properties of a specific system. This has proved especially useful for systems in which it is difficult to employ conventional methods to evaluate the mechanical properties. One example of that, is to use this principle to estimate mechanical behavior of a bilayered system of silicon nanocrystals (SiNC) deposited on a layer of polydimethylsiloxane (PDMS). Due to this unique combination of materials, conventional tests to evaluate mechanical properties, like uniaxial tensile or nano-indentation tests, cannot be performed. In this thesis, I employed the instability analysis for a bilayered system subjected to finite bending, to estimate the material behavior of the SiNC layer.In addition to studying instability in finite bending, I have developed a mathematical framework to study deformation and instability in a multilayered system undergoing unbending and eversion. First, I develop the solution of nonlinear elasticity to evaluate the change in geometrical parameters of the system due to deformation. Then, I solve the instability analysis to evaluate when a bifurcation occurs for a multi-layered system undergoing unbending or eversion. The solution for the instability problem is then obtained numerically by employing the compound matrix method.I have revealed that the stress states in a bilayered structure subject to unbending or eversion can result in the presence of multiple neutral axes, as previously observed in finite bending as well, or no neutral axes. Also, I found that the presence of a second layer significantly affects bifurcation behavior during unbending and eversion. Finally, I show that the presence of the stiff layer can significantly affect the bifurcation behavior just by moving the stiff layer from outside to inside in the reference configuration.