Nonlinear finite elements/Homework 11/Solutions/Problem 1/Part 15

Problem 1: Part 15: Finding the plastic flow parameterEdit

The discretized form of the Kuhn-Tucker conditions in conjunction with the consistency condition gives us

 

Use this condition and the relations you have derived in the previous sections to arrive at a nonlinear equation in   that can be solved using Newton iterations.

The yield function is

 

Therefore the discretized form of Kuhn-Tucker + consistency is

 

or,

 

Now,

 

Therefore,

 

Plugging into the discretized yield condition, we have

 

or,

 

Also

 

Therefore,

 

The nonlinear equation in   is