Nonlinear finite elements/Homework 11/Solutions/Problem 1/Part 12

Problem 1: Part 12: Trial elastic stressEdit

In the radial return algorithm, we define a trial elastic state as

 

where   are the stress and strain at   and   are the values at  . Show that, if the elastic response of the material is linear, equation (2) can be written as

 

From equation (2)

 

Therefore,

 

Hence shown.