Line search

Figure 143: 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:

$$\Delta \boldsymbol{u} \cdot \boldsymbol{R} (\boldsymbol{u}+ \lambda \Delta \boldsymbol{u}) = 0.$$ (451)

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 143), 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).