Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. One way to study these stresses is through the cantilever experiment, whereby a thin film is deposited onto the surface of a thin plate that is clamped at one end to a wall. The stresses that are generated in the film during drying are transmitted to the plate and drive bending. Mathematical modelling enables the film stress to be inferred from measurements of the plate deflection. The aim of this paper is to present simplified models of the cantilever experiment that have been derived from the time-dependent equations of continuum mechanics using asymptotic methods. The film is described using nonlinear poroelasticity and the plate using nonlinear elasticity. In contrast to Stoney-like formulae, the simplified models account for films with non-uniform thickness and stress. The film model reduces to a single differential equation that can be solved independently of the plate equations. The plate model reduces to an extended form of the Föppl-von Kármán (FvK) equations that accounts for gradients in the longitudinal traction acting on the plate surface. Consistent boundary conditions for the FvK equations are derived by resolving the Saint-Venant boundary layers at the free edges of the plate. The asymptotically reduced models are in excellent agreement with finite element solutions of the full governing equations. As the Péclet number increases, the time evolution of the plate deflection changes from $t$ to $t^{1/2}$, in agreement with experiments.

This note presents an elasto-capillary model of a cantilever subject to capillary stiction during drying process of removing sacrificial layers in MEMS. Similar to the dynamic analysis of the electrostatic pull-in of electrostatic micro actuators, the cantilever beam tends to be pulled down to the substrate due to the nonlinear capillary force with respect to the gap. The critical one-half gap deformation and the corresponding critical wetting area for pulling down a micro cantilever by surface tension are analytically found herein. The instability situation of a generalized critical deformation for power-law surface force with respect to gap is also predicted accordingly. Some prior MEMS works are exemplified to justify this critical one-half gap deformation for capillary stiction.

The flexural characteristic of a cantilever plate, which is heated from a fixed end, is considered and the effects of heat transfer on the plate are examined. The plate is heated with a temperature source while an excitation force is applied at the free end. Size of heat source is varied and temperature dependent properties of the plate are accommodated in the simulations. The finite element method (FEM) is adopted to determine the temperature field in the plate and flexural characteristics due to the applied impulsive load. It is found that the flexural characteristics of the plate change notably with the size of the heat source located at the fixed end of the plate. In this case, increasing the size of the heat source results in the enhancement of the amplitude and time shift in the flexural motion of the plate due to the heating and noheating situations.