A simple superposition solution for a point-loaded elastic plate on a soft substrate is proposed. The solution considers a "drumhead" being elastically bent into a compliant substrate that is viscoelastic-plastic. With simplifying assumptions it is found that the drumhead and substrate support loads proportional to δl/2 and δ 3/2, respectively, where δ is the vertical point displacement. At fixed displacement, relaxation proceeds at high loads, but if sufficiently unloaded, recovery or increased load results with time. Qualitative verification of the time-dependent drumhead solution is shown by relaxation and recovery data on polycarbonate covered by polysiloxane, composite or diamondlike carbon (DLC) coatings, and films.
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