Nonlinear finite elements/Homework11/Solutions/Problem 1/Part 14

Problem 1: Part 14: Return mappingEdit

Show that

 

We have

 

Now

 

The trace of the stress is given by

 

Therefore,

 

The stress-strain relation is

 

Hence,

 

Plugging into expression for  , we get

 

Therefore,

 

Remark: If we write the yield function as

 

then the above equation takes the form

 

These are equivalent.