It would take an elephant, balanced on a pencil, to break through a sheet of graphene the thickness of Cling Film I'm currently doing some work on a presentation about graphene, and have come across numerous articles which claim something along the lines of

It would take an elephant, balanced on a pencil, to break through a sheet of graphene the thickness of Saran Wrap / Cling Film.

My question is, is there any proof / calculations to back up this claim? Every article I come across seems to be very similar and I cannot find the original source which might contain proof, or a link the relevant paper/study 
Sources


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*http://www.dailymail.co.uk/sciencetech/article-2045825/Graphene-strong-sheet-clingfilm-support-elephant.html

*http://www.scientificamerican.com/article.cfm?id=balancing-act
 A: oh no! it appears I'm too late.. so this is a popular claim, and further popularized by Michio Kaku (youtube). Hover, graphene cannot be as thin as cling film. Why? because graphene by definition is an atomically thin substance! It's literally one layer of graphite, which is how it was discovered. Saran wrap is literally a million times thicker than a sheet of graphene. So, what happens if we stack graphene up to this thickness? We're back at graphite, and that thickness of graphite will not sustain the pressure of your foot, let alone an elephant!
Hypothetically, what if graphene was enlarged to a thickness of saran wrap, and was only an atom thick? Well, that's a silly question, because not even nuclear physics allows that possibility.
So that answer is: no.
A: The key here is not the Young's modules, which by the way is quite impressive as being 1 TPa, but the breaking strength of 130 GPa. It is these two combination that gives rise to the elephant story. 
Imagine you have a material that has very large Young's modules, but very small breaking strength, that would make it very brittle. A good example will be glass - you won't think an elephant would walk on a thin piece of glass... to the other extreme, if a material has very compilable, such as rubber band: it will be easy to stretch (small Young's modulus), but the elephant on it can easily stretch it so much to the point exceeds its (even big) breaking strength.
Therefore, the unique combination of large Young's modulus and large breaking strength makes this analogy reasonable. Of course, the assumed thickness is also crucial - without mentioning the thickness in the mm range, it won't hold the elephant either...
A: I think you are looking for something like this: 

We measured the elastic properties and intrinsic breaking strength of
  free-standing monolayer graphene membranes by nanoindentation in an
  atomic force microscope. The force-displacement behavior is
  interpreted within a framework of nonlinear elastic stress-strain
  response, and yields second- and third-order elastic stiffnesses of
  340 newtons per meter (N m–1) and –690 Nm–1, respectively. The
  breaking strength is 42 N m–1 and represents the intrinsic strength of
  a defect-free sheet. These quantities correspond to a Young's modulus
  of E = 1.0 terapascals, third-order elastic stiffness of D = –2.0
  terapascals, and intrinsic strength of σint = 130 gigapascals for bulk
  graphite. These experiments establish graphene as the strongest
  material ever measured, and show that atomically perfect nanoscale
  materials can be mechanically tested to deformations well beyond the
  linear regime.

So when Young's modulus of monolayer graphene is around $10^{12} \;\textrm{Pa}$, a back of the napkin estimate suggests that over a surface of $1 \;\textrm{mm}$ graphene can easily withstand $10^6 \;\textrm{N}$, which looks like a nice guess for an elephant several elephants to me :)
