Line search

Figure: Principle of the line search method

In the case of static calculations with face-to-face penalty contact the displacement increment \Delta \boldsymbol{u} in each iteration is scaled with a scalar \lambda in order to get better convergence. \lambda is determined such that the residual (i.e. external force minus internal force) of the scaled solution \boldsymbol{u} + \lambda \Delta \boldsymbol{u} is orthogonal to the displacement increment:

\Delta \boldsymbol{u} \cdot \boldsymbol{R} (\boldsymbol{u}+ \lambda \Delta\boldsymbol{u}) = 0. (539)

Now, the residual for \lambda=0 is known from the previous increment, and the residual for \lambda=1 is known from the present increment. In between a linear relationship is assumed (cf. Figure ), which yields the value of \lambda without extra calculations. With the *CONTROLS card the user can specify a value for \lambda_{\text{min}} (default: 0.25) and \lambda_{\text{max}}(default: 1.01).