Nonlinear finite elements/Homework11/Solutions/Problem 1/Part 8

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Problem 1: Part 8: Consistency condition - 2[edit]

The yield stress is given by the Johnson-Cook model

where is the initial yield stress, are constants, is a reference temperature, and is the melt temperature. Derive expressions for , and for the von Mises yield condition with the Johnson-Cook flow stress model.

The yield function is

Therefore,

and