312 



where £, ^nd £. are the meridional and circumferential strains, respec- 

 tively, given by 



'- a>r 





I- 



(10) 



(4) Similarity of Mohr circles . A fUrther relation is imposed on 

 the stresses and strains by the principle of the similarity of Mohr circles-^ 

 which, for the case treated here, may be expressed in the form, 



(b) Discussion of assumptions. — The equations of motion, Eqs, 

 (l) and (2), as has been stated before, are rigorously true in the limit of 

 vanishing thickness. If the stresses were linearly related to the strains 

 as in the elastic case, neglected bending terms would be proportional to 

 3, » However, in the plastic stress-strain relationship as expressed by 

 assumptions (2), (3), and (4), the bending terms are neglihible ^and conse- 

 quently Eqs. (l) and (2) hold over a wider range of thickness than in the 

 elas''"-ic case. 



The von Mises condition as expressed in assumption (2) can be 

 correlated only with biajdal tensile tests with plates,—' It implies a 



1/ Plasticity, by Nadai (McGraw-Hill, 1931). 



2/ The condition as written implies isotropy only with respect to di- 

 rections tangent to the plate making specialization to the linear 

 tensile test illegitimate. 



