Similarity relation upon the puncture of a thin sheet

Puncture is a break in a membrane (clamped on a distant peripheral outline) caused by pressing an indenter whose diameter is much less than the diameter of the membrane. Based on the measurements of the force P required for puncturing an aluminum foil over a wide range of relationships between its thickness h and the indenter radius R (for h/R = 0.12–7.00, i.e., from a blunt-indenter-thin-foil to a sharp-indenter-thick-foil case), we found a common nonlinear dependence of the dimensionless force P / EhR ∼ ( h /2 R ) n on the deformation of plastic bend in the contact h /2 R .