Crack Settings

This section needs writing. Below are some items that will be used or move else where.

In max energy release rate (or max hoop stress), the crack direction is at angle θ (which is ccw from self similar growth) and obeys

      [math]\displaystyle{ \cos\theta = {3K_{II}^2 + K_{I}\sqrt{K_I^2+8K_{II}^2} \over K_I^2+9K_{II}^2} \quad {\rm and} \quad \sin\theta = \mp\sqrt{1-\cos^2\theta} = \mp\left | {K_{II}\over K_I}(3\cos\theta - 1)\right| }[/math]

The second terms in negative or positive depending on K_II being positive or negative.