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How to explain the coefficient of Hill 48 yield criterion?

Submitted by Weijie Liu on

Can someone help me to explain the derivation of the coefficent ?

 

 In the paper "A theory of the yielding and plastic flow of anisotropic metals", the Hill 48 yield criterion:

  

 

The quadratic Hill yield criterion for thin rolled plates (plane stress conditions) can be expressed as: 

 

However,  in the book of "塑性・粘弾性" link: http://www.worldcat.org/title/sosei-nendansei/oclc/047515845

the Hill's  yield criterion was described as below.

 

 

Thanks.