Effective Strain of Frictionless Punch on Deep Plate

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I'm trying to figure out the effective strain of a frictionless punch on a deep plate. For simplicity's sake let's say it's in plane strain. Don't quite know where to start. Closest thing I can think of is the strain from a bulge test, but that involves a thin sheet. Looked at some indentor (Vickers, Brinell etc.) strains also, but these might not be applicable, since the indenter does not travel that far into the workpiece. I also looked at some of the literature concerning ballistics but they don't really report strain or how they calculated it. I feel like there's something very simple that I'm missing here.

I'd be grateful if someone could put me on the right path.
 
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Nidum said:
Shear stress .

I thought about doing σ = Ymε, but I don't have a value for Y!

[Edit] I suppose I could look it up, however
 
Draw me a diagram so that I can understand what your actual problem is .
 
Here you go
 
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I think you are actually looking at a plastic flow problem . There are various theory's regarding plastic flow in metals . Modelling real situations analytically is difficult and FE methods often have to be used . A not very accurate but sometimes useful approximate solution just assumes that all metal in zone around active end of punch is at yield stress .

Not the best of explanations but it's somewhere to start :

https://en.wikipedia.org/wiki/Flow_plasticity_theory
 
My inclination was to find P/2k from a hodograph and then use that pressure to solve for strain using th the formula I posted above. However I wasn't sure whether there was a commonly used formula or something based on the individual strains.