Crack Settings

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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} \qquad {\rm and} \qquad \sin\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.