Contact problem of a non-linear viscoelastic spherical membrane enclosing incompressible fluid between two rigid parallel plates

The process of using the atomic force microscopy to characterize the mechanical properties of various micro and nano structures requires better understanding of the contact problem of closed membranes enclosing fluid. This paper investigates the deformation of a non-linear viscoelastic, homogenous, and uniformly thin spherical membrane containing incompressible fluid between two rigid parallel plates. The Pipkin–Rogers non-linear single integral constitutive equation is used to model the membrane material. This includes Quasi-Linear Viscoelasticity (QLV) as a special case. The influence of various viscoelastic properties on the response is investigated. It is shown that, in a step deformation experiment, time dependence of the deformation indicates that the material should not be modeled using QLV.

► Contact mechanics for a non-linear viscoelastic fluid filled membrane.
► Non-linear viscoelastic force–deflection response.
► Influence of viscoelasticity on stresses and stretches.
► Influence of viscoelasticity on unloading response with relevance to nanoindentation.