Nonlinear finite elements/Homework11/Solutions/Problem 1/Part 13

Problem 1: Part 13: Trial elastic stressEdit

Starting from equation (3) show that

 

where   is the deviatoric part of   and   is the deviatoric part of  .

From equation (3) we have

 

The deviatoric parts of the stress and strain are

 

Therefore,

 

Now,

 

Therefore,

 

Hence

 

This shows that