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THEORY OF Tlii PLASTIC DEFORMATION OF THIN PLATSS 

 BY UNDERWATER EXPLOSIONS 



By John M. Richardson* and John G. Kirkwood^ 



ABSTRACT 



The theory of a plastic deformation of thin plates is worked out 

 for the case of axial symmetry. It is assumed that the stress-strain rela- 

 tions in the material are described by (a) vanishing strain for stresses 

 too small to satisfy the von Mises plasticity condition and (b) for stresses 

 satisfying the von Mises condition by incompressibility, and by the similar- 

 ity of Mohr circles. 



The linearized equations for the plate deformations are applied to 

 a problem of damage by underwater explosions. In Parts II to V, inclusive, 

 we consider in detail the deformation of circularly clamped plates without 

 cavitation in the water and we make comparisons with experiment. In Part VI 

 we consider the deformation of infinite plates with cavitation, and we at- 

 tempt to extend the results to the problem of contact e^qjlosions. 



^7 Physical chemist. Explosives Branch, Bureau of Mines, U, 3. Depart- 



ment of the Interior. 

 b/ Professor of Chemistry, California Institute of Technology, Pasadena, 



California, 



