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 δ 1/2 and δ3/2, 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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The authors would like to thank Professor David Bahr at Washington State University and Professor Trevor Page at Newcastle for discussions regarding the drumhead effect. We are pleased to acknowledge support from MTS Test Systems for A.S., by the Center for Interfacial Engineering under Grant NSF/COR-8721551 for K.Y. and L.C., and by ONR under Grant N00014-91-J-1998 for WWG. We would also like to thank Dr. Alex Hsieh of ARL, Aberdeen, Maryland for providing much of the material.