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

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Problem 1: Part 15: Finding the plastic flow parameter[edit]

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