192 



not strictly in accord with the facts. It would indeed be pleasant to be 

 able to relax some or all of these idealizations; however, it is clear that, 

 having recognized the artificialities for v/hat they are, it has been quite 

 necessary to invoke them in this paper in the name of mathematical simplicity. 



Equations (A) (B) (C), together with an eiipirically determined 

 stress-strain relation (analogous to (28) or (35)), specify completely the 

 motion and plastic deformation of any diaphragm of radius a, thickness h, 

 and initial velocity v. For instance, one may calculate the following: 



1. The radius R of the bending wave as a function of the time. 



2. The diaphragm profile at each instant. 



3. The thictaess distribution, 



4. Displacement - time curves of particles in the diaphragm. 



5. Stress and strain distributions, 



6. The center deflection as a function of v. 



7. The total time for the deformation to take place. 



The viewpoint presented here admittedly has led to a kind of short-cut 

 procedure which is designed to circumvent certain mathematical difficulties 

 inherent in a more rigorous theory. Because of this method of attack, it 

 may be necessary in the future, in order to make the results more generally 

 applicable, to reexamine some of the basic assumptions made herein. Out- 

 standing among these is the question of the initial radial velocity and stress 

 distribution (although the results seem to indicate that this has only a 

 slight effect on the final answer). Other investigations might consider such 

 effects as the magnitude of the energy absorbed at the bending wave, equili- 

 brium of the region behind the bending wave, and the possibility (which seems 

 small) of plastic flow in it, and the possible non-uniform radial flow and 

 tension in the central flat region, 



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