# Nonlinear finite elements/Homework 11/Solutions/Problem 1/Part 3

$\dot{\boldsymbol{\sigma}} = \boldsymbol{\mathsf{C}} : \dot{\boldsymbol{\varepsilon}}^e = \boldsymbol{\mathsf{C}} : (\dot{\boldsymbol{\varepsilon}} - \dot{\boldsymbol {\varepsilon}}^p)$
Plugging in the expression for $\dot{\boldsymbol{\varepsilon}}^p$ we get
$\dot{\boldsymbol{\sigma}} = \boldsymbol{\mathsf{C}} : \left(\dot{\boldsymbol{\varepsilon}} - \dot{\gamma}\frac{\partial f}{\partial \boldsymbol {\sigma}}\right)$