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

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Problem 1: Part 14: Return mapping[edit]

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.