Overview of the Different Chapters 163

In this thesis, the mechanical instability of thin film structure including buckling and wrinkling is investigated under applied compressive loading on the film. The effects of the loading on the system, the change in material properties of the film and substrate, the geometrical non‒uniformity of the system and other similar factors on the wrinkling pattern and its characteristic parameters such as wave number of the wrinkles and length of the wrinkles are considered. A summary of the results of different chapters are concluded in the following.

In chapter 3, the wrinkling of the film around an inclusion is considered. The inclusion is defined as a region on the film which applies compressive eigenstrain on the system locally and wrinkles develop around that region. For the inclusion line on the free standing film and deposited film on the substrate, it is shown that wrinkles develop on the film perpendicular to the inclusion line. The wrinkling parameters such as length and wave number of the wrinkles are derived in terms of loading parameters and material properties of the film/substrate. The results provide physical insight in modeling the suturing of the wound in surgical operations, the effect of the glue or other constraints on thin structures and so on.

Chapters 4, 5 and 6 mainly focus on the non‒uniformity of the system with finite length. The non‒uniformity arises due to the variation of the material properties as discussed in chapter 4, or the variation of the thickness of the film as presented in chapters 5 and 6. In fact, they show that for a non‒uniform film, wrinkles accumulate at

some specific locations while the other regions of the film remain unwrinkled. These specific locations of the film with accumulated wrinkles are the weakest locations of the system with thinner thickness or lower stiffness. Chapter 4 shows that unlike the homogenous films in which the wrinkles propagated along the entire domain, for a functionally graded material (FGM) film where the stiffness of the film changes with a continuous function along the length span of the film, wrinkles accumulate around the softest region of the film. It also provides simple explicit expressions for the wrinkling parameters such as wave number and effective length of the film influenced by the wrinkles. High sensitivity of the wrinkling parameters with the FGM gradient parameter shows the importance of the proposed model in this work. Chapters 5 and 6 represent similar results for wrinkling of a non‒uniform film with variable thickness. They show that for different profiles of the film thickness, the wrinkles accumulate at the thinnest position (or positions) of the system. This conclusion becomes more significant for thin film systems where the uniformity of the film cannot be guaranteed due to the tiny thickness of the system. High sensitivity of the wrinkling accumulation around the thin positions of the system intensifies the importance of the analysis.

On the other hand, in contrast with other works in the literature, the effect of finite length of the film has not been considered on the wrinkling pattern based on the best knowledge of the author. In fact, researchers focus on the wrinkling of the film with infinite length while the wrinkles propagate uniformly all over the system. However, the results of this thesis show that for a finite length film, the wrinkles are constrained at the edges of the film and the pattern of the wrinkling drastically changes. The finite length model proposed in this work provides more compatibility with real applications of the wrinkling in thin film technology.

In order to investigate the amplitude of the wrinkling after instability, a nonlinear analysis is presented in chapter 7. The post‒wrinkling analysis shows how the amplitude of the wrinkles increases by increasing the applied compressive load on the wrinkled film. Moreover, it illustrates that there is a threshold for amplitude and compressive load on the film such that, beyond the threshold value, the wrinkling is substituted by folding of the film at some special points. The post‒wrinkling parameters and the effect of

non‒uniformity of the system on accelerating the wrinkling‒folding transition phase are investigated.

Chapter 8 considers the effect of the substrate on the wrinkling pattern of the film. The effects of the surface elasticity and residual surface stress are considered on the wrinkling of the film. Also, a non‒uniform model for the substrate is proposed and the accumulative effect of the wrinkling on the soft regions of the substrate is considered.

The results of different chapters represent some clear insights in the physics of wrinkling of thin film structures. They consider the effect of the non‒uniformity of the system with finite length on the wrinkling parameters by proposing explicit expressions in terms of the loading and structural parameters and show the accumulation of the wrinkles at some special positions. In other words, they provide adequate insight in the physics and mechanics of wrinkling of thin film structures.