MCE Ph.D. Thesis Seminar
A bilayered system is an assembly of two diﬀerent materials and has the form of ﬂat and thin layers. The two materials are attached to each other at the surface. The attachment method varies depending on the materials properties. Bilayered systems made of materials with diﬀerent dimensions and stiﬀness have been widely studied and used for diﬀerent applications. The characteristic scale of this kind of system can go from hundreds of km in the case of geological layers on the Earth surface to some µm in the case of very small electronic systems or microlenses.
The behavior of a bilayered system, when submitted to stimulus, is characterized by the conﬂict between the preferred response of each material and the constraint that one imposes on the other. As a result the deformation of the bilayered system will be diﬀerent from what could be obtain with the materials taken separately. Of particular interest is the buckling of such systems: when submitted to a particular stress distribution, one material will expand highly more than the other but as the two materials are attached at the interface surface, the material displacements must be continuous through this interface. The conﬂict between the continuity of displacement and the need to expand diﬀerently may result in nonlinear patterns at this interface. Those unstable situations can be used to deﬁne a limit of constraint for the materials or can be used as actuators for a desired surface pattern. Many studies have focused on characterizing homogeneous buckling within an entire surface due to homogeneous strain distribution within the top surface. This characterization was performed theoretically, numerically and experimentally. But some studies have shown diﬀerent possibilities of evolution of the so far known buckling patterns. As a consequence, several questions appear: Is there a possibility to modify non linear patterns regardless of what is imposed by mechanical properties and dimensions? What happens in the case of non uniform state of constraints within the bilayered system?
This thesis explores those questions for the case of a thin stiﬀ ﬁlm attached to a compliant thick substrate. The ﬁrst part of this thesis serves to describe the initial buckling theory in the case of uniform strain and it is explained how to deﬁne the loading treshhold resulting in uniform buckling at the surface characterized by a ﬁnite number of spatial frequencies.The second part of the thesis studies the consequences of a nonuniform loading within the surface. A numerical method based on the theory of the ﬁrst part is implemented to show the emergence of new frequencies due to the discontinuous loading distribution. The third part focuses on the possibility to tuning a uniform buckling by including an electromechanical coupling into the bilayered system. This coupling makes the materials sensitive to electric ﬁelds thus creates a new energy term to interfere with the mechanical energy of deformation thereby modifying the resulting spatial frequency of the buckling. This study is done theoretically and numerically by ﬁnite element modeling.