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

Problem 1: Part 11: Discrete Kuhn-Tucker

The Kuhn-Tucker loading-unloading conditions are

$\dot{\gamma }\ge 0,f(\mathit{\sigma },\alpha ,T)\le 0;\dot{\gamma }f(\mathit{\sigma },\alpha ,T)=0.$

Write down a discrete form of the Kuhn-Tucker conditions.

The discrete form of the Kuhn-Tucker conditions is

$\begin{array}{cc}\mathrm{\Delta }\gamma & \ge 0\\ f({\mathit{\sigma }}_{n+1},{\alpha }_{n+1},T_{n+1})& \le 0\\ \mathrm{\Delta }\gamma f({\mathit{\sigma }}_{n+1},{\alpha }_{n+1},T_{n+1})& =0\end{array}$