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

where R = K_II/K_I. The second terms in negative or positive depending on K_II being positive or negative. In the limit of K_I to zero, cos θ = 1/3 for crack direction of -70.5 (or +70.5) degrees.