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 = {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 term is 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. This method requires K_I and K_II which can only be done for isotropic materials (and their subclasses).

in cod hoop direction, the code uses the max energy release rate method, but assumes R = δ_t/δ_n or the sliding and opening crack opening displacements. This can be used for any material.