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

Problem 1: Part 8: Consistency condition - 2Edit

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