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

Problem 1: Part 11: Discrete Kuhn-Tucker
The Kuhn-Tucker loading-unloading conditions are

\dot{\gamma} \ge 0 ~, f(\boldsymbol{\sigma}, \alpha, T) \le 0 ~; \dot{\gamma} f(\boldsymbol{\sigma},\alpha,T) = 0 ~. $$ Write down a discrete form of the Kuhn-Tucker conditions.

The discrete form of the Kuhn-Tucker conditions is

{ \begin{align} \Delta\gamma & \ge 0 \\ f(\boldsymbol{\sigma}_{n+1}, \alpha_{n+1}, T_{n+1}) & \le 0 \\ \Delta\gamma~f(\boldsymbol{\sigma}_{n+1}, \alpha_{n+1}, T_{n+1}) & = 0 \end{align} } $$