I want to know an object's (in this case, the plastic) "tolerance" to being pierced until it gets pierced.
Knowing the modulus is not good enough. LDPE behaves non-linearly and inelastically in large deformations, so the OP must be able to describe the large-deformation inelastic response of the material. In addition, knowing this response is not sufficient for defining the failure behavior of the material. That is an entirely different functionality involving the invariants of the stress tensor.OP, you could research the modulus of LDPE.
In my judgment, you are grossly underestimating the complexity of this problem. This involves the large-deformational solid mechanics behavior of a highly non-linear material experiencing an extremely complex concentrated contact loading. The rheological behavior of the material must be described by much more than just a modulus, or even a modulus and Poisson's ratio, and the response will not even be purely elastic. Just the job of experimentally quantifying the rheological constitutive behavior of the material for an arbitrary general deformation (using simpler deformational kinematics) would be quite daunting. Even if this behavior were quantified experimentally using appropriate rheological constitutive equations, the analysis of the deformation and stresses in this very complicated loading problem would be mathematically complicated, and would require the use of finite element computational software to solve.Right, and I think to do that he would have to measure the strain of the bag or the stress being applied to the bag in order to use the modulus. That would find the limit of its linear range. Which is why I asked the OP what was in the bag because that is applying stress to it.