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Understanding the generation of mechanical stress in drying, particle-ladenfilms is important for a wide range of industrial processes. The cantileverexperiment allows the stress in a drying film that has been deposited onto athin plate to be quantified. Mechanical stresses in the film are transmitted tothe plate and drive bending. Mathematical modelling enables the film stress tobe inferred from measurements of the plate deflection. The aim of this paper isto present simplified models of the cantilever experiment that have beenderived from the time-dependent equations of continuum mechanics usingasymptotic methods. The film is described using nonlinear poroelasticity andthe plate using nonlinear elasticity. In contrast to Stoney-like formulae, thesimplified models account for films with non-uniform thickness and stress. Thefilm model reduces to a single differential equation that can be solvedindependently of the plate equations. The plate model reduces to an extendedform of the Foppl-von Karman (FvK) equations that accounts for gradients in thelongitudinal traction acting on the plate surface. Consistent boundaryconditions for the FvK equations are derived by resolving the Saint-Venantboundary layers at the free edges of the plate. The asymptotically reducedmodels are in excellent agreement with finite element solutions of the fullgoverning equations. As the P\'eclet number increases, the time evolution ofthe plate deflection changes from $t$ to $t^{1/2}$, in agreement withexperiments.

Time-dependent modelling of thin poroelastic films drying on deformable plates